My wife is working on a guide for new translators to the book of Galatians. She and her colleague have been grappling with the account of Paul confronting Peter. The usual interpretation of "You are a Jew, yet you live like a Gentile and not like a Jew" is that Paul says to Peter "You accept freedom from the Jewish law for yourself, why not give the Gentile believers the same freedom".
My wife and her colleague are thinking there is another interpretation. Maybe Paul is using 'Jew' in this phrase to mean 'a true person of God'. In Romans 2:28-29 he says a true Jew is not just an outward Jew, with a physical descent from Abraham and a physical circumcision; but one who is Jewish inwardly, circumcised in heart by the Spirit. So what would a 'true Gentile' be? Someone uncircumcised in heart, whether they were outwardly non-Jewish or even outwardly Jewish.
Maybe his accusation of Peter is saying "When you withdraw from eating with your Gentile brothers, you are reinstating the separation that Jesus died to end. You are uncircumcizing your heart and acting like a Gentile in heart, even though you are a physical Jew."
This sounds complicated. But I do think it makes a bit more sense of the next couple of verses. "If I rebuild what I destroyed, I prove that I am a lawbreaker. For through the law I died to the law so that I might live for God." (Gal 2: 18-19). I've always been puzzled by "if I rebuild what I destroyed", and thought it must mean when Paul repents of sins and attempts to restore relationships with people he'd sinned against, that is rebuilding what he had destroyed. That would mean "through the law I died to the law" is a new thought. But maybe the two are one thought. Maybe Paul means "If I rebuild as a requirement the Jewish law, which I once had died to through my faith in Jesus' death and resurrection, I have become a transgressor". Maybe Paul is imagining himself in the position Peter took briefly, to display what a bad mistake it would be to bring back the law as a requirement.
One thing that does seem clear to me. When Peter separated himself from the Gentile believers, he had forgotten the exhortation from the voice in his vision, "Do not call anything impure that God has made clean." (Acts 10:15).