I just want to offer my 2-cents worth here, as I’m not likely to participate in further discussion for now.
Paul is clearly upset when writing the letter Galatians --- a letter almost entirely focused on the issue of circumcision. The dismayed Paul accuses the waffling Galatians of being bewitched (3:1), and he wishes that those bothering his group on the issue would not only remove the tip, but the whole works (5:12).
The Galatians are strongly focused on becoming heirs of Abraham, honorary sons of God, and full participants in the Israel of God. Paul had apparently led them to believe they could achieve those ends without the messy ritual of circumcision, but rather by faith in his now heavenly, spiritual son of the Jewish God as a redeemer from the law. Apparently after Paul had left, some had swayed the group --- likely by the extremely clear and unequivocal requirement for circumcision in the Jewish scriptures. So they really wouldn’t need Paul after all.
Nearly all of the letter Galatians is focused on the issue of circumcision, and on Paul’s authority. When Paul opens the letter with an accusation that the group is turning to a “different gospel” than what he had preached to them --- of course he is referring to their interest in getting circumcised.
For Paul to give-in on the question of circumcision for his partner Titus, even for a short period of time, so that “the truth of the gospel would be preserved” (Galatians 2:5), is contradictory in spades to the tone of the entire letter.
… to whom we did not yield in subjection even for a time, so that truth of the gospel would be preserved with you. (Galatians 2:5)
Originally read like this before being interpolated with the addition of οἷς οὐδὲ, as suggested ---
… we did yield in subjection even for a time, so that truth of the gospel would be preserved with you. (as suggested by some)
This suggested reading basically throws the core argument in the letter under the bus, and I think the suggestion of such an interpolation and interpretation reveals a misunderstanding of both Paul and of the letter Galatians.
On the other hand, for Paul to claim the leaders in Jerusalem did not require the Greek brother-in-the-faith Titus to be circumcised (Galatians 2:3), and that Paul did not yield to the pressure from the “false brothers” (2:4) --- all that makes perfect sense in the context of Paul’s letter so that “the truth of [Paul’s] gospel would be preserved” (Galatians 2:5).
The analysis cited in the post directly above (end of p. 1), to which I am only partially responding here, demonstrates once again the dangers of using the later legends in Acts to understand Paul.