There exist groups who believe that Christians or believers of Jesus completely replaced Jews as Israel and as the chosen people, and that Jews no longer have a valid relationship with G-d, unless they become Christians.
Is such a theology prevalent within Christianity? What is the scriptural basis both for and against it?
You kind of tipped your hand by using the word ideology in your question! An unscriptural ideology is at the heart of a deficient theology regarding Israel and the Christian Church. (By Church, with a capital C, I'm referring to the universal or "holy catholic" church, which is composed of all true believers in Jesus Christ.)
There Is No Legitimate Argument For It!
The key biblical passage in this regard would have to be Romans, chapters 9-11, where Paul attempts to counteract an incorrect ideology with a correct theology. By the way, if you entertain any thoughts about Paul having slipped into ideology instead of theology, read 9:3-5.
"For I could wish that I myself were accursed, separated from Christ for the sake of my brethren, my kinsmen according to the flesh, who are Israelites, to whom belongs the adoption as sons, and the glory and the covenants and the giving of the Law and the temple service and the promises, whose are the fathers, and from whom is the Christ according to the flesh, who is over all, God blessed forever. Amen" (Italicized words are original to the NASB Updated version).
What Paul is saying, in part, is there would be no Christianity without Judaism. According to Paul, Judaism is the very foundation of Christianity. Most significant, of course, is that Jesus was born a Jew!
Most Evangelical Christians I know do not subscribe to the notion that Israel is washed up, or that God has given up on Israel and subsequently turned to the church as his only light of truth in a dark world. They focus, rather, on the very expressions Paul uses to indicate the temporary nature of Israel being put on hold, so to speak. Paul uses such expressions as
". . . it is not as though the word of God has failed" (9:6)
In other words, the word of God may not have had the effect God desired, but that is not to say it will never achieve God's desired outcome.
". . . the children of promise are regarded as descendants" (9:8; notice the tense of the verb I've italicized: present--not past--tense).
Put differently, descent from Abraham, the father of faith and a nation, will on day--once more--be an advantage to those descendants who believe God.
Let's stop here. In Paul's line of reasoning, what God was doing among Israel is simply being continued today through the church until the promises God made to Abraham and Isaac, "the child of promise," are fulfilled completely.
The Christian Church as Parenthetical
Think of the "church age" as parenthetical. Not in the sense that what is inside the parentheses is unimportant or an afterthought. No, but in the sense that what came before the parentheses is going to be continued after the parentheses. Other expressions Paul uses are also of relevance:
". . . but Israel , pursuing a law of righteousness, did not arrive at that law . . .. Because they did not pursue it by faith, but as though it were by works. They stumbled over the stumbling stone" (and then Paul quotes Isaiah 8:14). Note: the italicized words are in the the NASB Updated version.
Put differently, Israel stumbled at the simplicity of simply believing in the promise of God; namely, that he was going to bless the entire earth through Abraham's seed (and Isaac's seed, and King David's seed, and so on). Israel got caught up in the rigid observance of the Law as their way of earning God's favor with works of righteousness and stumbled at the sufficiency of faith to win God's favor, which is at the heart of the biblical notion of grace (viz., God's undeserved, unmerited favor to sinners, whether Jew or Gentile).
". . . there is no distinction between Jew and Greek; for the same Lord is Lord of all, abounding in riches for all who call on Him; for 'WHOEVER WILL CALL ON THE NAME OF THE LORD WILL BE SAVED'" (10:12-13).
Another key verse is the following:
". . . God has not rejected His people, has He? May it never be! For I . . . [Paul] am an Israelite . . ." (11:1 NASB Updated).
"In the same way then, there has also come to be at the present time a remnant according to God's gracious choice" (ibid., v.5, original italics)
"But by their [Israel's] transgression salvation has come to the Gentiles, to make . . . [Israel] jealous. Now if their transgression is riches for the world and their failure is riches for the Gentiles, how much more will their fulfillment be!" (ibid., v.12, original italics).
In other words, a time of fulfillment is coming for Israel. Again, that fulfillment comes after the parentheses of the church age.
Israel Is the Cultivated Stock; the Gentiles, A Wild Branch Grafted In
Paul also resorts to metaphor in chapter 11, talking of bread dough, trees, and branches. The Jews are the original tree root of the cultivated olive, whereas the Gentiles are the "wild" branches which were grafted into the tree when the original branches were "broken off" (vv.16-17). He then warns the Gentiles not to become arrogant. After all, the Jews came first. Just because some of their branches were broken off doesn't mean the original root can't or won't come back to life and produce more branches from the original root!
Moreover, God can just as easily break off the grafted-in branches (i.e., the Gentiles) for unbelief when they fail to lay hold of God's kindness while it is still offered to them (see vv.18-24).
A Partial and Temporary Hardening
Finally, Paul wraps up his argument by saying,
". . . a partial hardening has happened to Israel until the fullness of the Gentiles has come in; and so all Israel shall be saved, just as it is written [in Isaiah 59:20]."
Furthermore,
". . . the gifts and the calling of God [to Abraham, Isaac, and Jacob, and so on] are irrevocable. . . .For God has shut up all in disobedience so that He may show mercy to all" [both Gentile and Jew] (v.32).
In conclusion, God has not replaced Israel with the Christian church; rather, the Christian church was grafted in as a way of continuing what God had been doing all along with Israel (viz., seeking a people for himself who would latch on to his promises and thereby be declared righteous by God through simple faith, just as Abraham's faith was accounted unto him as righteousness (Romans 4:3 and 9), since "the just shall live by faith."
The arguments for the position of Replacement Theology start in places like..
And all the people answered, “His blood be on us and on our children!” Matthew 27:25
It is further developed by some in saying that the promises given to Abraham have been totally transferred to thr church, vis a vis, Galatians 3:14.
Thus, it is said by them, that all unfulfilled promises to Israel are given to the church, as is the example of the "Rest" of Hebrew 4:8, "Therr remains, therefore, a rest for thr people of God." Snice natural Israel did not enter into that rest, and since God's Word cannot return void, it is given to the believers. The church.
The issue, at hand, however, is that is often read as "The Gentile Church", and there exists no entity in Scripture.
There has to be a proper balance here. Paul lays out the case concerning natural Israel in Romans 10-11.
Paul had just finished explaining how he wished he could be cut off and Israel saved. However, he finished by saying that the very thing the Jews were seeking is both what the Gentiles did achieve and the Jews, in general, failed to. And, his reason was Faith.
So then, after this, Paul continues to express the current condition. He says ththat his prayer is that they will be saved, that is, come into the church, but that there is no difference in how both the Jew and thr Gentile must approach God. It isn't in what you do, ascend to heaven, or desend to hell, it is the Word of Faith in our mouths.
Paul's thesis for this is found, then, in Ephesians 2:14-16.
For He Himself is our peace, who made both groups into one and broke down the barrier of the dividing wall, by abolishing in His flesh the enmity, which is the Law of commandments contained in ordinances, so that in Himself He might make the two into ONE NEW MAN, thus establishing peace, and might reconcile them both in one body to God through the cross, by it having put to death the enmity.
Ephesians 2:14-16, capitals added.
Paul's phrase "One New Man" thus describes the condition Jesus brought about. Paul, back in Romans 11, thus describe it as an Olive tree. Certain Jews, natural branches, we're broken off, and wild Olive brances, Gentile believers, were grafted in.
Thus, Paul's statement is that there is no more separation, but that the root of the tree is the Jewish Nation. He also warns the Gentiles not to Lord it over the Jews, since they too could easily be replaced by the original if they became conceited.
There is not a "Jewish church" and a "Gentile church", just as there is not a Jewish Gospel and Gentile one. Paul's entire argument hinges that God has grafted Gentiles into the same rootstock as the Jews, and there is now only one. For believers.
What is clear is what Peter said in Acts 2, "Now there is therefore no other name given under heaven whereby men might be saved". Again, in Hebrews, it says, "How shall we escape if we neglect so great a salvation."
So, when asked if the "Jews" have a special place with God, if you refer to the non-believing Israelite, no, they must come to faith in Messiah, the church of God. The church is not a "parenthesis", as dispensationalists claim, is is Christ's soon to be wife! That He paid for with His blood.
If, however, you are asking about the "Jew", who is the child of Abraham by faith in Jesus, then they have are no longer enemies with God, but are reconciled through Jesus.
All this bearing true, with the exception that God has promised the ultimate regathering of the Jews, where He will no longer hide His face frome them, but will pour out His Spirit upon thr nation as a whole. Ezekiel 39:28-29. This, as Paul wrote, will be national salvation, as the entire nation as a whole believes in Messiah, Jesus Christ of Nazareth, and comes at the end of the Gog/Magog war (Ezekiel 38-39). All Israel will be saved.
This is why, earlier in Romans, Paul wrote, for the Gospel's sake they are the believer's "enemies", but for the "election"s sake, God's choosing, they are loved.
Even as the prophets said that so long as seed time and harvest continued, they would always be a nation in His sight, He has not let them go. However, the "Time of the Gentiles" will come to a close (Luke 21) with the restoration of Jerusalem, and they will all be regathered and born again in Yeshua, with Jerusalem most likely as the chief church in the world.
Proponents of total replacement theology tend to minimize the enduring promise and election towards Israel, while those in dispensadispensationalists camps minimize and dismiss the unification of the Jew and Gentile spoken directly in Ephesians 2:15, above.
In groups still maintaining a complete dismissal of the Jews in election are Full Preterists, who maintain that no promises remain for the nationalistic Jews.
While all believers are heirs to the blessings of Abraham, it does appear that the nationalistic and land promises, concerning the perpetuirty, the election, and the land of Israel, are promised to the people, and not merely the "believers".
God still has lovery for, and plans, for the Jewish people, but it is only, and ever, in the name of His Son Jesus, even as He testified that it was their very Scriptures, all of which testified directly of Him.
REPLACED OR REDIFINED?
When we talk about ‘replacement theology’, we are using very emotive language. The idea that God has ‘replaced’ Israel with the (largely gentile) Church, suggests a betrayal’ of the promises made by God to the patriarchs.
Therefore, the word ‘replacement’ may not be the best one to use to describe what God is doing through the Church. Paul clearly distinguishes between what he calls ‘Israel after the flesh’ (1 Cor 10:18) and ‘the Israel of God’ (Gal 6:16). These two groups however are not mutually exclusive. Many who are now part of the first group (physical Jews) are also, now, or will be in the future, part of the second group (the true Israel), composed of believing Jews and believing gentiles alike.
It may be better to think of Israel as being ‘redefined’ by the Gospel of Grace, rather than ‘replaced’.
THOSE WHOM GOD FOREKNEW
In other words, as Paul asserts: “God has not cast away his people which he foreknew…” (Rom 11:2). God has always intended for the many physical descendants of Jacob to be called to faith in Christ. However, their initial rejection of the Gospel provided an opportunity for the gentiles to be called and to become part of the true Israel of God, something which God had also intended from the very beginning: “For whom he did foreknow, he also did predestine to be conformed to the image of his Son…” (8:29).
PREDESTINED TO BE CALLED
The idea of predestination (admittedly a difficult concept) flows through the argument Paul makes for Israel in Rom 9-11, the most startling revelation, which springs from this doctrine, being that “…they are not all Israel, which are of Israel…” (Rom 9:6) and that “…they which are the children of the flesh, these are not the children of God, but the children of the promise are counted for the seed” (8). So, according to Paul, not all of the descendants of Jacob (not all Jews) are actually part of the true Israel of God, but, as with the gentiles, only those 'predestined' to be called in this Church age.
THE TRUE PEOPLE OF GOD
So, what the apostle is saying is that, being a physical descendant of Abraham, Isaac and Jacob (or, for that matter, being physically circumcised) means nothing, in terms of belonging to the people of God; for, as he states in another place: “…he is a Jew who is one inwardly, and circumcision is that of the heart, in the spirit not in the letter; whose praise [the name Judah means ‘praise’] is not from men, but from God” (2:29).
ALL ISRAEL WILL BE SAVED
To put is simply, and in Paul’s terms, there is a remnant of the physical people of Israel who have been called to faith at this time (11:5), however, all who have been predestined (Jew and gentile alike) will ultimately find themselves as part of the Israel of God and be saved (11:26).
Michael Horton sums it up like this: "So God is not unfaithful. His Word has not failed, even if we do not currently see the Jewish people embracing Christ en masse. The prophets consistently taught that Israel would be saved through a remnant, and that this Jewish remnant would also include a remnant from all the nations...The people resulting from this unconditional election would constitute the true Israel" (Michael S. Horton: Article: Remnant-Who Is Israel http://modernreformation.org/default.php?page=printfriendly&var1=Print&var2=41)
Scriptural basis for replacement ideology/theology
1 Thessalonians 4:17 Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord.
Paul had every hope and expectation that he would see the return of Jesus and the establishment of the kingdom. ("we which are alive")
As time progressed people began to wonder about what happened to Israel. As they considered their church tradition and the Bible they searched for some explanation. It is natural to look for a transition between what was and what is. Many would look at Pentecost and see a transition from Israel to "the church" (something mostly without Jews).
The diaspora seemed pretty good evidence that Israel was no longer a factor to be considered. Without the forward looking of a solid eschatology, it would be difficult for people to see themselves as other than the culmination of God's plan.
Even today many say they do not believe in replacement theology, but see no role for a restored Israel. You have a de facto "replacement" doctrine when a future fate of Israel is not considered.
Replacement theology was an idea in search of support. It was not a doctrine derived directly from scripture. An occasional verse could be found that was unflattering about Israel, but by and large doctrines that ignored Israel had a much wider acceptance than those who specifically declared Israel as no longer in the picture. While not technically declaring Israel "replaced", all of the references to prophecy about Israel could be appropriated by the church. Although this sometimes called for theological nimbleness.
An approximation can be found for those who see no role for Israel overlapping with those not inclined to look for a millennial kingdom on earth. Thus the support that is presented for things like Preterism and amillennialism can also be sometimes used by those much fewer who declare that the church has replaced Israel.
Salvation was never based on Jewishness. Israel is the only "nationally elected" nation. Salvation is by "individual election." There is no reasonable grounds to make the church a replacement of Israel. There is however strong literal evidence that the national election of Israel must still be in effect because of the everlasting covenant between Abraham and God.
If all of the first coming promises to Israel were literally fulfilled then all of His second coming prophecies should be expected to be fulfilled. Yeshua (Jesus) will return to Israel only when Israel asks Him to. Hosea 5:19
... Jews no longer have a valid relationship with G-d, unless they become ChristiansI don't think this is really an accurate representation of most (or perhaps any) Christian theology. Can you point us to a specific group which believes this? That would make it easier to address the question. Otherwise, I'm inclined to believe this question is likely based on a misconception about Christianity...