Galatians is an interesting story. First, scholars do not know exactly where Galatia is. Or even if it is one location or several locations clustered together. This makes it difficult to know which people Paul is addressing.
We should not try to read into the Bible our opinion but continue to pray that God will reveal to us what is needed. Still, we can learn a lot from the first reading. Peter and Paul had their differences. Paul was to go to the Gentiles. Peter would continue work with the Jewish people.
Peter would waffle back and forth with the dietary laws. When he was with Jewish people, he followed the Jewish customs of not eating pork or other unclean animals. When he was with the Gentiles I wonder if he enjoyed bacon. Paul challenges Peter on this. Even with small matters we need to be spiritual leaders to all peoples.
We must be consistent with what we teach and what we preach. In other words, we need to walk the talk we talk. This could have entered into a serious division for the fledgling faith, but Paul and Peter sat down and talked this out.
I admire the humility of Peter. He realized he was in the wrong and changed. I admire Paul because he knew Peter was the leader, the authority figure, yet he came to Peter and pointed out the inconsistency of not his teaching but the example he was demonstrating. That took courage.
Through the leadership of the Holy Spirit, the two faith leaders came together to make this new Christian faith stronger. Through their example we can learn to work things out. Prayer, honestly, and respect go a long way. Trusting one another, that we both want to do is best, must be recognized. We can work it out!
May the Lord bless you in the name of the Father and of the Son and of the Holy Spirit. Amen