Christ is not divided and believers are Christians no matter what they were before.
Look at Paul condemning Peter for showing distinction in Christ between Jew and Gentile and applying that separation that the old law demanded. Paul is calling people by what they were formally so he can point out the problem.
11 But when Cephas came to Antioch, I opposed him to his face, because he stood condemned. 12 For prior to the coming of certain men from James, he used to eat with the Gentiles (no distinction); but when they came, he began to withdraw and hold himself aloof, fearing the party of the circumcision. 13 The rest of the Jews joined him in hypocrisy, with the result that even Barnabas was carried away by their hypocrisy. 14 But when I saw that they were not straightforward about the truth of the gospel, I said to Cephas in the presence of all, "If you, being a Jew, live like the Gentiles and not like the Jews, how is it that you compel the Gentiles to live like Jews?
15 "We are Jews by nature(OT God's people) and not sinners from among the Gentiles (OT not God's people); 16 nevertheless knowing that a man is not justified by the works of the Law but through faith in Christ Jesus(saved), even we have believed in Christ Jesus, so that we may be justified by faith in Christ and not by the works of the Law; since by the works of the Law no flesh will be justified(sinner/lost). 17 But if, while seeking to be justified in Christ(Faith), we ourselves have also been found sinners(Old Law because it can't save), is Christ then a minister of sin? May it never be! 18 For if I rebuild what I have once destroyed, I prove myself to be a transgressor. 19 For through the Law I died to the Law, so that I might live to God. 20 I have been crucified with Christ; and it is no longer I who live, but Christ lives in me; and the life which I now live in the flesh I live by faith in the Son of God, who loved me and gave Himself up for me. 21 I do not nullify the grace of God, for if righteousness comes through the Law, then Christ died needlessly."
Righteousness doesn't come by the Law. Is it true that a person could never be saved by observing the Law (OT)?
Peter's problem wasn't that he kept the Law, but that even in that he didn't he would imply to the Gentile either that they were not saved, could not be saved, or were not included among the people of God, in that he withdrew fearing the party of the circumcision... which did compel the Gentiles (believers or unbelievers here?) to live like Jews (which is not a requirement in Christ). The problem was not in living like the Jews, but the hypocrisy of Peter created confusion. Meaning, observing God's Law is fine... but making it appear like you have to be a Jew to be saved or be called among God's people, justified, is communicating the wrong message.
1 Corinthians 7:18 NASB - 18 Was any man called when he was already circumcised? He is not to become uncircumcised. Has anyone been called in uncircumcision? He is not to be circumcised.
So this is my perspective.
Remember what Paul said here?
1 Corinthians 9:16-23 NASB - 16 For if I preach the gospel, I have nothing to boast of, for I am under compulsion; for woe is me if I do not preach the gospel. 17 For if I do this voluntarily, I have a reward; but if against my will, I have a stewardship entrusted to me. 18 What then is my reward? That, when I preach the gospel, I may offer the gospel without charge, so as not to make full use of my right in the gospel. 19 For though I am free from all men, I have made myself a slave to all, so that I may win more.
20 To the Jews I became as a Jew, so that I might win Jews; to those who are under the Law, as under the Law though not being myself under the Law, so that I might win those who are under the Law; 21 to those who are without law, as without law, though not being without the law of God but under the law of Christ, so that I might win those who are without law. 22 To the weak I became weak, that I might win the weak; I have become all things to all men, so that I may by all means save some. 23 I do all things for the sake of the gospel, so that I may become a fellow partaker of it.
And here?
Philippians 3:3-16 NASB - 3 for we are the true circumcision, who worship in the Spirit of God and glory in Christ Jesus and put no confidence in the flesh, 4 although I myself might have confidence even in the flesh. If anyone else has a mind to put confidence in the flesh, I far more: 5 circumcised the eighth day, of the nation of Israel, of the tribe of Benjamin, a Hebrew of Hebrews; as to the Law, a Pharisee; 6 as to zeal, a persecutor of the church; as to the righteousness which is in the Law, found blameless.
7 But whatever things were gain to me, those things I have counted as loss for the sake of Christ. 8 More than that, I count all things to be loss in view of the surpassing value of knowing Christ Jesus my Lord, for whom I have suffered the loss of all things, and count them but rubbish so that I may gain Christ, 9 and may be found in Him, not having a righteousness of my own derived from the Law, but that which is through faith in Christ, the righteousness which comes from God on the basis of faith, 10 that I may know Him and the power of His resurrection and the fellowship of His sufferings, being conformed to His death; 11 in order that I may attain to the resurrection from the dead. 12 Not that I have already obtained it or have already become perfect, but I press on so that I may lay hold of that for which also I was laid hold of by Christ Jesus. 13 Brethren, I do not regard myself as having laid hold of it yet; but one thing I do: forgetting what lies behind and reaching forward to what lies ahead, 14 I press on toward the goal for the prize of the upward call of God in Christ Jesus. 15 Let us therefore, as many as are perfect, have this attitude; and if in anything you have a different attitude, God will reveal that also to you; 16 however, let us keep living by that same standard to which we have attained.