You've posed a good question.
Many Protestant, evangelical churches, whether independent (non-denominational) or denominational, tend to do two things which, although not necessarily biblical in the strictest sense of the term (i.e., according to the "chapter and verse" method of proof-texting), tend to draw fairly clear doctrinal lines in the sand.
First, they construct a "What We Believe" statement which generally speaking covers the non-negotiables of the faith. Second, they tend to administer discipline on church members and regular attenders (or even on visitors who sow discord among the assembly) who "proselytize" for doctrines which either clearly contradict their churches' "What We Believe" statement or tend to create disunity through needless controversy.
Lines Drawn In the Sand
A typical "What We Believe" statement would say in effect,
If you want to become a member or regular attender of our church [e.g., Main Street Community Church" or "First Presbyterian Church of Anytown"], these are the beliefs which provide and promote unity among us, and we title that list "What We Believe" [or "Doctrinal Statement of Faith," or some such title]
Obviously, each church will likely have a different number of non-negotiables, but I suspect that if you were to compare each and every "What We Believe" statement of all the Protestant, evangelical churches worldwide, you would find remarkable unity in what they consider to be the non-negotiables of the Christian faith.
In part, I suggest, this unity can be traced not only to the clear teaching of the Word (more on that later), but also to the various councils from the distant past which settled such non-negotiables as the deity of Jesus Christ (for example) and are identified by the name of a particular controversy or doctrinal heresy traced to false teachers such as Arius (Arianism), Pelagius (Pelagianism), and Sabellius (Sabellianism), to name but three.
Even though I have not done such a comparative study of the type I've suggested, I suspect the top six would include the following (in no particular order):
The Deity of Jesus Christ (i.e., Jesus Christ was, is, and ever shall be God in the flesh, his deity confirmed by his having been conceived by the Holy Ghost in the womb of the virgin Mary)
The Trinity (i.e., God exists in three persons, each of whom is fully divine: God the Father, God the Son, and God the Holy Spirit)
Salvation (i.e., the vicarious, substitutionary death of Jesus Christ on the cross provides forgiveness of sins and a full and free salvation to all who believe if they simply by faith call upon the name of the Lord. Furthermore, there is salvation in none other besides Christ)
God's Word (i.e., the 66 books of the Bible comprise God's final, complete, Holy-Spirit inspired and authoritative revelation of all that is needed for Christian faith and practice). [While the definition of inspiration may vary somewhat from denomination to denomination, the unifying factor in most Protestant, evangelical churches is that the Bible is authoritative and, rightly interpreted, is an infallible guide for faith and practice]
The New Birth (i.e., one's entrance into the kingdom of God is by regeneration only, which the Bible describes as being born again, born from above, or born of the Spirit of God)
The Return of Jesus Christ (i.e., Jesus Christ will return to earth to do battle with evil and defeat it once and for all, ushering in a new heaven and a new earth, free forever from sin and death and the corrupting effects of the Fall)
These five "articles of faith" comprise at least some of the salient biblical criteria for unity within any given church or denomination within Evangelicalism.
Three Strikes and Yer Out!
Second, most Protestant, evangelical churches administer discipline on an ad hoc basis. That is, they wait for a situation to arise in which the unity of the local assembly is being threatened by either blatant sin and/or false teaching. The Scriptures pertaining to blatant sin are plentiful, and I needn't refer to them. As for false teaching: again, a good "Statement of Faith" aids the church leadership in detecting and dealing with false teaching, which always tends to disrupt the unity of a local assembly, if not an entire denomination!
In the church in which I am currently a member (and have been for about 17 years), a brother was stirring things up by attempting to convince some church members that our church's doctrinal stand regarding Divine election was wrong. Our church, by the way, does not take a stand in its Doctrinal Statement on all five points of Calvinism (viz., Total Depravity, Unconditional Election, Limited Atonement, Irresistible Grace, and Perseverance of the Saints), though it would certainly agree with most--if not all--of them to some degree.
If the gentleman had simply "shared" his point of view with other church members, there would not likely have been an issue. Because he was "proselytizing" for his point of view and insisting that the church leadership was incorrect in their interpretation of Divine election, however, he was brought before the elder board (the "ruling board" of our church, with the Senior Pastor as its titular head), warned, and put under discipline for an unspecified amount of time (meaning: he would continue to be a member in good standing as long as he stopped 1) proselytizing for his point of view, and 2) accusing the church leadership of teaching and preaching false doctrine).
There is not necessarily a single “proof text” which churches use to encourage (and sometimes “enforce”) the unity of the body regarding doctrinal differences; rather, there are many. Safe to say, however, the tenor of the teaching of the New Testament regarding unity within the Body of Christ (both Universal and local) can best be summed up, I suggest, in the following saying:
What are the “essentials” of the faith? Again, that depends on a given church’s “Statement of Faith.” I’m assuming, by the way, that most churches do have one. Whatever their statement comprises, however, the clear teaching of the Bible in general, and the New Testament in particular, is that unity in essentials is of primary importance, since as you point out, “a house divided against itself cannot stand.”
What are the non-essentials of the faith? Again, that depends on a given church’s “stand” on the kinds of issues the apostle Paul addressed in Romans 14 and 15, and in I Corinthians 12, for example. Usually these types of issues are culturally derived and change from generation to generation. What was once taboo in most Evangelical churches within certain denominations (and sometimes in different geographical regions within a denomination!) at one time in history may no longer be taboo years later.
What unifies Christians regardless of what they consider taboo is the clear teaching of Scripture that Christians are to “abhor what is evil, and cling to what is good” (even though good and evil may be defined, operationally, in slightly different ways).
In conclusion, rather than list all the Scripture passages I could think of to provide you with biblical bases for defining unity and its opposite, I’ve opted just to outline in perhaps a simplistic way how the tenor of Scripture regarding unity and its opposite is in a sense perhaps more important than a list of specific, chapter-and-verse proof texts.
Perhaps Jesus’ high-priestly prayer in John 17 summarizes uniquely well the kind of unity God expects of His Church, and the primary reason for unity within His Church.
"I do not ask on behalf of these alone, but for those also who believe in Me through their word; that they may all be one; even as You, Father, are in Me and I in You, that they also may be in Us, so that the world may believe that You sent Me (vv.20-23 NASB, my emphasis).
Based on the tenor of Jesus’ teaching in that prayer, the purpose of unity within the Body of Christ is primarily to attract non-believers to His Church, since God proffers his love, grace, and mercy to all people from every people-group (from Gk. ta ethne, the “nations” from Jesus' Great Commission to all believers in Matthew 28:18-20).
Where the world tends to divide people (whether according to color, religion, national origin, sex, socio-economic status, intelligence, culture, language, age, or a host of other criteria or rubrics), the Church of God is to embrace all comers who, regardless of how the world may pigeonhole them, believe in Jesus in accord with the teaching of the apostles (i.e., "through their word,” to which Jesus alluded in his high priestly prayer, above).