I'm new here but for more than 45 yrs I have done extensive research on the Bible and related matters.
I. MAINSTREAM BASIS AGAINST LDS & JWs
Mainstream churches generally [very general usage here] believe that they are Bible based. The major reasons given are:
a. Most Mainstream churches believe in 1 God with 3 co-equal "heads".
b. LDS believes there are many Gods.
c. JWs believe that God & Jesus are separate Gods.
a. Most Mainstream churches beleves all believers go to Heaven.
b. LDS believes believers become Gods & some get their own planets.
c. JWs think only 144,000 go to Heaven, the rest stay on earth.
a. Most Mainstream churches believes Jesus is the Son of God.
b. LDS believes Satan is Jesus' brother.
c. JWs believe Jesus is a created being & is now Archangel Michael.
a. Most Mainstream churches hold that the Bible is from God (although some add the Apocrypha &/or oral traditions).
b. LDS's main book is the Book of Mormon along with other extra-biblical books.
c. JWs have their own Bible, the New World Translation in which verses have been altered or stressed to support their own beliefs.
a. Many Mainstream churches hold that Jesus is the only mediator between man and God.
b. LDS believes that Joseph Smith is a modern day "prophet" who restored the "church" back to its proper place with the truth restored.
c. JWs have their "Watchtower" Society **Governing Body" providing their scriptural interpretation. They made several wrong prophecies in the 20th century, which they explain away in one way or another.
a. The Catholic church (& some related churches) holds that other books and traditions are just as important or even more important to their worship, such as the Apocrypha or lost books and doctrines (i.e. Popes, Infallibility on the throne, Catechism, Assumption of Mary, Immaculate Conception, Veneration of Saints, Rosary, Creeds, etc.) that are beyond the reach of the 66 legitimate Bible books.
b. LDS beleifs also include books that go beyond the reach of the genuine 66 Bible books. Many of their beliefs have dependancy on the Book of Mormon, Pearls of Great Price and Documents & Covenants, in which it is claimed that gold plates were found in upstate New York, Jesus came to America, Adam & Eve and the Garden of Eden were in Missouri, etc.
c. JW's have their own Bible in which at least some verses have been altered to support their beliefs. A good deal of their beliefs are dependant on what is written in their Watchtower magazine.
II. REAL BASIS AGAINST LDS & JWs
Actually, the "basis" for what is non Christian is clearly defined in the Bible. The problem is it takes a lot of work to find and lay out a proper, well-defined basis for determining what is and is not rightly Bible based. While many "mainstream" [general broad use here] have determined that neither Mormons (LDS) nor Jehovah Witnesses (JWs) are Christian, a number of them lack true understanding even of their own misinterpretation(s) of what is real Christian teaching (i.e. Trinity Doctrine error -See below under Comment 2).
I believe that to fully answer the posed question requires one to establish a basic set of facts, the Bible foudation & purpose and common sense rules for reasoning out what should be accepted as the truth. Our approach, coming from our human condition, experience from surrounding environmental events and our actions/reactions (cause & effect), our human imperfections (seen and unseen), etc., may make all the difference for drawing a "right" conclusion or failure thereof (we may have to set aside some preconceived ideas, notions, prejudices and/or assumptions). The following might help point us in the right direction:
Since the Bible is the primary reason and basis for Christianity's existence I believe we ought to turn to the Bible to see what it says:
1. BIBLE PROOF
Most important: Is the Bible true?
(ESV) Prov. 30:5 Every word of God proves true; he is a shield to those who take refuge in him.
6 Do not add to his words, lest he rebuke you and you be found a liar.
(most Christian [broad label usage here] and several other religions have stated (or implied) their claims/beliefs are based on, come from the Bible and/or they are associated with the Bible and/or the Bible can be used along with their beliefs/claims and practices but are they wrong? We need to go to the Bible to determine what is true.)
2. JESUS, THE SON of GOD?
The second most important question is: Is Jesus the Son of God or not? Jesus' statement:
John 14:6 Jesus said to him, “I am the way, and the truth, and the life. No one comes to the Father except through me (see Acts 4:12; Jn 5:39).
Either this statement is true or there is no God (He either knows all or He can't be God). In this statement Jesus is making it quite clear that He is much more than just another great teacher. Since Jesus made this statement I thought it is more important to first find out if what He said is true rather than trying to sift through piles of information, books and statements made about Jesus and the Bible.
3. FALSE TEACHERS & PROPHETS
The Bible mentions false prophets (to be a false prophet you must also be a false teacher).
Acts 13:6 When they had gone through the whole island as far as Paphos, they came upon a certain magician, a Jewish false prophet named Bar-Jesus.
2 Peter 2:1 But false prophets also arose among the people, just as there will be false teachers among you, who will secretly bring in destructive heresies, even denying the Master who bought them, bringing upon themselves swift destruction.
Gal 1:8 But even if we or an angel from heaven should preach to you a gospel contrary to the one we preached to you, let him be accursed.
4. JUDGMENT
A proper approach for establishing which is which requires one to find right teaching starting from no. 1 above and also by process of elimination to expose wrong Bible teaching as we find them (if we intend not to be mislead - false teaching has great consequences).
John 7:24 Do not judge by appearances, but judge with right judgment.”
Many believe the Bible says don't judge at all but when carefully read you will find the Bible message actually warns against making wrong or false judgments. Every time you go to cross a street you must judge where and when to cross. All day long we make many judgments as to what we should do.
5. DO NOT ADD OR OMIT THINGS
I found that many do not carefully read what is actually written in the Bible. For instance, many missed the fact that plants were created before the sun and stars. The reason is explained in other Bible text. For every claim made the whole Bible must be taken into context.
1 Cor 4:6 I have applied all these things to myself and Apollos for your benefit, brothers, that you may learn by us not to go beyond what is written, that none of you may be puffed up in favor of one against another.
Gal 3:15 To give a human example, brothers: even with a man-made covenant, no one annuls it or adds to it once it has been ratified.
Deut 4:2 You shall not add to the word that I command you, nor take from it, that you may keep the commandments of the Lord your God that I command you.
6. MAN'S WAYS & IDEAS
I also observed that many make the mistake of believing what others claim is true especially if they have a position perceived as having authority to make such claims.
Jer 10:23 I know, O Lord, that the way of man is not in himself, that it is not in man who walks to direct his steps.;
Prov 14:12 There is a way that SEEMS right to a man, but its end is the way to death.;
Hosea 4:6 My people are destroyed for lack of knowledge; because you have rejected knowledge, I reject you from being a priest to me. And since you have forgotten the law of your God, I also will forget your children.;
Micah 7:5 Put no trust in a neighbor; have no confidence in a friend; guard the doors of your mouth from her who lies in your arms;
Matt 7:21 “Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but the one who does the will of my Father who is in heaven.
22 On that day many will say to me, ‘Lord, Lord, did we not prophesy in your name, and cast out demons in your name, and do many mighty works in your name?’
23 And then will I declare to them, ‘I never knew you; depart from me, you workers of lawlessness.’
There is a number of other factors, etc. to add to the above but it would take many pages to go into exhaustive detail. I could have spent all my spare time studying all religions to the last detail but filling my head with volumes of useless information, I most likely would never have found out who our God actually is nor who His Son is. There is a verse (I can't remember where it is) that states something like: They gather much knowledge but they'll never find the truth.
Back to the original question: Mormons, JWs and other saw that there was to be a reformation but misunderstood that it was not the New Testament that was at fault (nor the Old Testament either). Mormons, JWs and others did not understand we cannot make up a new "covenant" and that God should honor it. They did not understand that the NT covenant is the final and eternal covenant, superseding all other covenants. Jesus is perfect and so is His new covenant, needing no changes - Both God and Jesus never change. God deliberately set up the old covenant with one major flaw, one that only sending His Son to earth could remedy.
While many "mainstream" churches can readily see the more blatant reasons, "a basis" for why something is wrong with the beliefs of Mormons and Jehovah Witnesses, many do not have a full understanding of why they and others have been and are wrong in many of their beliefs. Perhaps this is a subject for another discussion.
If any claimed "Christian" (again broad usage here) is coloring outside the Bible text and its parameters they are acting outside God's and Jesus' definition and instructions for how to be a genuine Christian in Their eyes. The Bible is all about right and wrong. The wise will keep making it their goal to better comply with its instruction while others will keep looking for justification for whatever suits them, what tickles their ear.
-Edits:
(For comments - Thanks Caleb -I hope this is OK. I added answers because I have a lot to say and some sites do not give one a lot of space to write, more being allowed in an answer.)
Being new here, I can't post a comment so I'm posting more answers (in addition to my original answer) with regard to comments (disreqard -adding it to my original answer).
@ Nelson (1st comment):
I'm not new to LDS beliefs (also, I have even been to the Salt Lake City temple). Before you read my comments please take the time to carefully reread my previous list of Bible references.
Actually, most "standard" Bibles (some are better at doing it) have been mostly properly translated (for the most part, most discrepancies are relatively minor to very minor). Once you become somewhat familiar with the Bible you can compare verses from other versions. However, God is smarter than us and knew some would try to twist the meaning and/or the word itself so He protected His word. He used an unchangeable system (in redundancy) that forever binds the OT&NT truth that never changes.
Other than some mutilation of scripture text (which would make it too obvious that something was done to it at least to the wise), as long as properly translated Bible text exists to be compared to, the truth can't be obscured to those genuinely looking for it.
Whether Joseph Smith was well-meaning or not he added things that were never in the Bible (Jesus was never in America nor were Adam & Eve in Missouri). Any new "vision" must line up exactly with what was written in the Old & New Testament. It cannot vary even one degree. Apparently, Smith was unaware of this.
Jer 23:28 Let the prophet who has a dream tell the dream, but let him who has my word speak my word faithfully. What has straw in common with wheat? declares the Lord.
The fact that the Book of Mormon exists indicates to those who are wise and have even just a good knowledge of the Bible text that it does not conform to what is written in the Bible, that is it is non-Biblical by its very existence. There is no such thing as a God authorized "another testament" nor will there ever be.
The truth is complete, fully contained within the Bible itself. It is why we are warned and instructed to not go beyond what is already written in the Bible itself. Clearly, Smith proves by his writings, whether he intended to or not, that he went far beyond what he thought he perceived as misinterpretation of the Bible text.
The problem is that the more Smith got off in his own direction and misinterpretation the more he compounded the false claims he started with. Whereas, a true reformation would have come by starting with and staying with what was instructed in the Bible. In other words, misinterpretation was because of human error and by their relaxing their guard and/or becoming lazy instead of staying the course, making sure what they taught and did was securely in line with Biblical teaching.
It was not due to the Bible being wrongly translated or just being misinterpreted, which Smith did not understand. Just because you can confess with your lips that Jesus is our Redeemer it does not mean that your heart is not far away from the truth of who Jesus is nor how to follow Him (truly, from within your heart not by more of an outward or mechanical motion or what you think Jesus wants from you or wants you to do).
Isaiah 29:13 And the Lord said: “Because this people draw near with their mouth and honor me with their lips, while their hearts are far from me, and their fear of me is a commandment taught by men,
These verses also apply to Isaiah 29:13:
Matt 7:21 “Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but the one who does the will of my Father who is in heaven.
22 On that day many will say to me, ‘Lord, Lord, did we not prophesy in your name, and cast out demons in your name, and do many mighty works in your name?’
23 And then will I declare to them, ‘I never knew you; depart from me, you workers of lawlessness.’
James 2:19 You believe that God is one; you do well. Even the demons believe—and shudder!
The point is that lots of people think that Jesus is the Son of God. It does not mean that they really know Him. Rather, they know of Him, that He probably existed or even that He did exist, not much else, especially on the proper personal level.
@ Nelson (2nd comment):
III. TRINITY DOCTRINE
At this point I think its best to put forth the actual God, Jesus and the Holy Spirit's correct relationship as the Trinitarian concept is in fact incorrect as are other concepts concerning this matter. Perhaps we can then more easily see whats wrong with other beliefs. These things are hard to understand. The correct relationship is as follows:
Jesus is the Son of God, Lamb of God and King of kings=He has Deity as His Father has =we are to also worship Him but Jesus isn't His Father: The Trinity Doctrine (TD) is wrong (NOTE [for those told otherwise]: the word Bible doesn't affect interpretation-the TD does). Unfortunately, people CONFUSE TRUTH (this offends many)/HATE.
The TD claims there are 3 CO-EQUAL heads=1 God. However, if the 3 are not equal the TD does not and cannot apply - its null and void. Sadly, people use only a few verses and/or are not careful to read verses in whole Bible context. 1 Cor 4:6 =don't add or omit things from the Bible text:
The TD (as are other concepts) is a roadblock to true Bible interpretation (In part the Catholic church got the TD idea from Pagans. Others [ie. JWs, lds, islam, moonies and others] figured out the TD is in error but they did not know our true God, Son and Holy Spirit relationship)=they didn't know Jesus (as their claims indicate). They never rightly went to nor learned to trust and rightly follow Jesus. Who knows more about a house, the Builder or people whom moved in later?
1. JESUS:
Jesus is God's Son [His Word not God's Body {Christ's Spiritual Body =believers in Him} =John 1:1], equals the pure essence of God [He was and is not an angel as JWs claim -Heb 1:2-6] neitehr when in flesh nor in Heaven. Jesus was not replacing nor was He ever equal to His Father (see John 5:30; Phlp 2:6-7; Col 2:9). Jesus (His Spirit existed with God from before the universe existed) is the closest we get to know infinite God in flesh (only a vessel =God's 1st creation part -something like being God's voice-box -not just some created being as LDS and JWs believe) to deliver eternal truth in person -John 14:7 (stoops to our level so to speak).
Born of human woman (for His earthly mission), Jesus is a separate person-entity (He has His own soul [what makes a person an individual] and given a human body -and Mary ISN'T God's mother) but God gave Jesus authority to be treated as His Father (conceived of God's Holy Spirit =fullness of DEITY [He deserves worship -Matt 14:33; 28:9] -SIR-NAME God =Jesus' birthright, reward as God's Son and to sit at God's right hand). In conception, God and Mary gave part of each to Jesus' life.
To rightly know Jesus starts at John 1:1. W/o a language God couldn't reason, know His thoughts, create a universe, life nor talk to others. So Jn 1:1 names Jesus as God's language. Created in God's image, man has the same limits. Despite how primitive most organisms need language to function and live with others.
Your language (always part of you) can't usurp your authority, act on its own and never tells you what to do. Therefore, Jesus' claims are true (Jn 5:19,30; 8:28) -a student is never greater than his teacher. Your words pass understanding of you to your son. If your son learns all you teach him, he in effect becomes like/is you for all intents and purposes. For obeying you, you can reward him the highest position, your authority.
A father owns a business and teaches his son to run his business. He goes away and puts his son in charge, trusting he'll run it just as he would. If the son obeys and runs the business as the father did, in effect he's his father and can claim to be his father =like father, like son -while exactly like his father he's never equal to him even thoegh he has his father's authority. The same is true for God and His Son, whom fully did God's will not His own so His Father gave Him right to also be worshiped:
Rom 5:19 Adam's sin made many sinners but by Jesus' obedience many are to be righteous.
REF: Jn 12:49; 14:28-29; Lk 6:40; Col 1:15 -Jesus is in God's image by rightly obeying God; Heb 5:7-8; Lk 2:52 -Mk 13:32; 20:23; Phil 2:6; Jn 17; 15:1 =God NEVER BECAME His Son.
2. GOD:
Only one GOD can occupy infinity =God of Israel =no other legit gods exist (HE CAN'T DIE EVER and doesn't fit into an earthly body). God has ULTIMATE AUTHORITY Jesus and the Holy Spirit do not have. Only God knows the day and hour for the end -Mt 24:36 and appoints who sits with Him. God has a soul like us (makes Him an individual -ie. a cell nucleus only Spiritual). All 3 are 1 in Spirit [of God] but Jesus and the Holy Spirit submit fully to God. Being 1 doesn't apply to difference in authority =the TD does not apply.
As long as 1 true full 360 degrees (in all directions) infinity exists (which the Bible proves it exists) two or more full infinities cannot exist nor can two Gods occupy the same infinity. Only a Spirit can occupy true full infinity. Everything having physical properties is measurable. Infinity cannot be measured.
3. the HOLY SPIRIT:
The Holy Spirit is God's "Spiritual body" (God is Spirit -to be 100% pure the Holy Spirit [no form] MUST occupy true infinity (360 deg. in all directions) =no flaws, =always existed -you can move over or make a space within Yourself to create a univeerse separate from yourself and create borders & rules where you want them). The Holy Spirit acts on God's command:
Jn 16:13 When the Spirit of truth comes, he will guide you into all the truth, for he will not speak on his own authority, but whatever he hears he will speak, and he will declare to you the things that are to come.
God's body, voice & ears act on God's will -same for our body). The Holy Spirit can be called "He" (generic) as you can be called he(even if your ID is known). The Holy Spirit is more than deliverer of God's power, works and the word through Jesus (Jn 1:1-5; 4:23). Only the eternal truth, forever unchanged keeps God perfect =SEAMLESS Garment.
The point is many religious people started off with wrong beliefs, trusted in misinterpretations told to them along the way. Some started religions, often never double or triple checking what they thought was true or they allowed their desires and agendas or other influences to rule their decisions, some intentionally. Many well-meaning people were taken in along the way. Over many centuries many followed suit. Many zeroed in on few wrong things and made the mistake of not making the Bible an every day guide for correction of things overlooked by those around them. Will we do the same or will we check everything even if we thought some things were right up to now?
Many a religious organization will continue down wrong paths no matter what is told or shown to them. Some stay their course and perhaps patch a few things or even claim they have received new light or revelations but the wise will find the real path to Jesus. The point is the truth is complete within the Bible. Anything extra-Biblical regarding changing God's and Jesus' actual Biblical teaching is wrong by its very existence.
@ Nelson (3rd comment):
Again, because the Trinity Doctrine is wrong, it does not follow nor justify one making a whole new or different non-Biblical concept nor does it make them legitimate. Unfortunately for LDS, there are so many things that they believe and do that have nothing to do with actual Bible concepts, it makes LDS, in its entirety, false and fully beyond actual Biblical teaching.
The only way out of such a mess requires that those who want to follow our real God and Jesus get out of false religion and seek our real Jesus with all their heart and soul. Sadly, many will never do that, deciding not to step out of what has become a security and comfort zone for them (false though it is).
Jesus said, "Do not judge by appearances but judge with right judgment." (Jn 7:24). He did not say not to judge at all. The real Bible message is: Don't judge for wrong reasons nor judge to make yourself look better than another or for the purpose of lording it over others or for the sake of judging. There are those who will not make judgments simply because they do not want to upset the apple cart or buck the "status quo" but the wise want to learn the true purpose for what Jesus taught.
@ Daniel (4th comment):
Because someone's beliefs and claims are in part or in whole wrong does not mean they cannot see "holes" in another's beliefs or claims (and yes sometimes they may have their judgment wrong in whole or in part). It would be better if they would carefully examine their own beliefs to weed out what they got wrong from various sources but many won't. If one is wise, they won't allow themselves to get caught up in wrong teaching as they do not want to be mislead. Sadly, both the LDS and the JWs (and others) got so far away from what the Bible actually says I doubt that either would be willing to dump their entire teaching and start over. The same goes for many mainstream churches. Thanks for looking that verse up for me.