Paul rebuked peter because Peter (being a Jew) began to shun the gentiles because he wanted to fit in with his own people the Jews. Peter was wrong at that time. Both Peter AND Paul preach the same gospel so I don't see what your point is of all of this. Peter was not a bridge man, if you read his book of the bible it is the same gospel as the rest of Scripture.
This is what your talking about:
Ga 2:11 ¶ Now when Peter had come to Antioch, I withstood him to his face, because he was to be blamed; for before certain men came from James, he would eat with the Gentiles; but when they came, he withdrew and separated himself, fearing those who were of the circumcision. And the rest of the Jews also played the hypocrite with him, so that even Barnabas was carried away with their hypocrisy. But when I saw that they were not straightforward about the truth of the gospel, I said to Peter before them all, "If you, being a Jew, live in the manner of Gentiles and not as the Jews, why do you compel Gentiles to live as Jews?
Peace frodo
This is Paul's version of what happened and how he argued against Peter and him casting blame on others shows his blatant stance against such personnages. It was his debating tactics and not the scripture that he used to create support for his own stance. What sort of a claim is this that if one eats with non-Jews then his way has become like the way of non-Jews? It is a fallacious argument and no one was allowed to write in at the time why it was so simply fallacious. Simple fact is that to entice people to the way of God one must dine with them and be brotherly to them. Then in time when they accept the creed matters then they will emulate the outer forms also. There is no double standard that Paul has so cleverly made to seem exists here.
Here is what Barnabas says in the last verse of his Gospel:
222 After Jesus had departed, the disciples scattered through the different parts of Israel and of the world, and the truth, hated, of Satan, was persecuted, as it always is, by falsehood. For certain evil men, pretending to be disciples, preached that Jesus died and rose not again. Others preached that he really died, but rose again. Others preached, and yet preach, that Jesus is the Son of God, among whom is Paul deceived. But we, as much as I have written, that preach we to those who fear God, that they may be saved in the last day of God's Judgement. Amen.
Reference to Paul being deceived is also in the Dead Sea Scrolls.