My $0.02 on this subject: I think we should take seriously the statement that Peter was “fearing the party of the circumcision” after receiving news from James’ men. It may be that Peter received news of a credible, substantial threat to the safety of his table fellowship. It would certainly comport with the hostility and martyrdom Yeshua believer’s were suffering during that time. It’s easy for modern believers to forget or underestimate just how dangerous the situation was back then.
Peter would then have to decide whether or not he wanted to endanger the lives, not just of his fellow Jews, but also his Gentile guests whom he may have considered as “innocent bystanders” he didn’t want hurt. Paul saw things differently. He had more exposure to gentile believers and knew they were just as willing and capable to ensure hardship for Yeshua. He also had an intimate knowledge of anti-Yeshua zealots and knew how important it was to not back down to them.
A thought experiment: Suppose a messianic synagogue hosts a public seder one Passover and, as a sign of goodwill, several prominent Muslims and mainstream Jews in the community agree to be guests. A week before the Seder, a terrorist threat is phoned into the synagogue demanding claiming reprisal if the seder goes through. What do you do as Rabbi? Do you cancel the event or disinvite the guests to avoid potential bloodshed, or do you take a stand against troublemakers? There’s reasons for either decision, just like Peter and Paul both had their reasons for the stances they took.
Of course, there’s not much historical clarity in the context of the Paul’s Galatians epistle and the so-called Antioch incident, so I’m open to different views on the issue.