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The issue to which Paul referred in the Galatian letter was one of the most important aspects to get right (Judaising threatened to turn the whole salvation by faith alone into a works based off-shoot of the fallen into works religion of the Judaisers), especially since the split from Judaism was so vital at that stage in the early church.

Gal 2:Paul Opposes Cephas
11 When Cephas came to Antioch, I opposed him to his face, because he stood condemned. For before certain men came from James, he used to eat with the Gentiles. But when they arrived, he began to draw back and separate himself from the Gentiles because he was afraid of those who belonged to the circumcision group. The other Jews joined him in his hypocrisy, so that by their hypocrisy even Barnabas was led astray.
14 When I saw that they were not acting in line with the truth of the gospel, I said to Cephas in front of them all, “You are a Jew, yet you live like a Gentile and not like a Jew. How is it, then, that you force Gentiles to follow Jewish customs?
15 “We who are Jews by birth and not sinful Gentiles know that a person is not justified by the works of the law, but by faith in Jesus Christ. So we, too, have put our faith in Christ Jesus that we may be justified by faith in Christ and not by the works of the law, because by the works of the law no one will be justified.
17 “But if, in seeking to be justified in Christ, we Jews find ourselves also among the sinners, doesn’t that mean that Christ promotes sin? Absolutely not! If I rebuild what I destroyed, then I really would be a lawbreaker.[ Paul is telling us right there why it was important for him to stand against the split starting to occur with this once again spearating themselves from the Gentiles ... Peter of all men should have known better, having been given the vision which allowed him to go into the Gentile House of Cornelius, to share the Gospel of Grace. The Church that Jesus established, the spiritual Church, has no distinctions between Jew and Gentile. All are reconciled by Grace alone, not of any works as the Judaisers were trying to inveigle the Gospel.]
19 “For through the law I died to the law so that I might live for God. I have been crucified with Christ and I no longer live, but Christ lives in me. The life I now live in the body, I live by faith in the Son of God, who loved me and gave himself for me. I do not set aside the grace of God, for if righteousness could be gained through the law, Christ died for nothing!”

What Peter and other Jewish converts were doing was sliding back into the exclusivity of Judaism, with the misapplied works under the law. We see the same error in cahtolicism today. And we see what it is doing, so we know in Paul's time it must have been pretty important to cut it off.