Paul let Peter have it right between the eyes and Peter repented because he had let himself be influenced by Other high ranking preachers in the Church who were presumably also in error. The Church did not split into two camps and form two denominations the Church of the circumcision and the Church of the non-circumcision.
Peter repented and they went to Jerusalem and fixed it then and there.
I have found a good passage on this and I'll paste it here.
For three Chapters Paul is worked up over the Corinthians having divided themselves up as the disciples of different apostles and teachers. Paul flat tells us that only the carnal (self serving) and babes would ever think such a thing. At the end Paul concludes that we are not disciples of any teacher preacher apostle of prophet but we belong to Christ, He purchased us with his blood. And right in the beginning Paul asked was Paul crucified for you. This is critical that we understand that we can only be the disciples of one – that is Jesus Christ. And if we make ourselves the disciple of another as Eve did in the garden when she became a disciple of the serpent we are no longer Christ’s. Eve heard the voice of another, she believed the words of another, she was obedient to the words of another, she taught the words of another, and then she made disciples of her master.
Paul tells us here he laid a foundation – he then issues a clarification and a warning of men building foundations by saying Take heed for no other foundation can one lay but Jesus Christ. And then Paul issues an even sterner warning that God will destroy anyone that defiles the temple with a foundation other than Jesus Christ and Paul concludes this lesson on discipleship reminding us that the pastor teachers apostles and prophets like the world like life and death like the things present and like the things to come are all to be our servants and we are to serve none of them or become the disciples of none of them because we are Christ’s.
I Corinthians 1:11-14 For it hath been declared unto me of you, my brethren, by them which are of the house of Chloe, that there are contentions among you. Now this I say, that every one of you saith, I am of Paul; and I of Apollos; and I of Cephas; and I of Christ. Is Christ divided? was Paul crucified for you? or were ye baptized in the name of Paul? I thank God that I baptized none of you . . . .
1 Corinthians 3:1-3 And I, brethren, could not speak unto you as unto spiritual, but as unto carnal, even as unto babes in Christ. I have fed you with milk, and not with meat: for hitherto ye were not able to bear it, neither yet now are ye able. For ye are yet carnal: for whereas there is among you envying, and strife, and divisions, are ye not carnal, and walk as men?
1 Corinthians 3:4-6 For while one saith, I am of Paul; and another, I am of Apollos; are ye not carnal? Who then is Paul, and who is Apollos, but ministers by whom ye believed, even as the Lord gave to every man? I have planted, Apollos watered; but God gave the increase.
1Corinthians 3:10-11 For I have laid the foundation, and another buildeth thereon. But let every man take heed how he buildeth thereupon. For other foundation can no man lay than that is laid, which is Jesus Christ.
1 Corinthians 3:17 If any man defile the temple of God, him shall God destroy; for the temple of God is holy, which temple ye are.
1 Corinthians 3:22-23 Whether Paul, or Apollos, or Cephas, or the world, or life, or death, or things present, or things to come; all are your's; And ye are Christ's; and Christ is God's.
This is a lot more far reaching than circumcision and it is here with us today in spades.
It doesn't take a deep theological insight to see that.