It seems as though Paul is using a sort of sliding scale of holiness to determine who can be part of the movement. Following the Law to the letter is the absolute on one end and pagan idolatry is on the other. However, within this scale it is not necessary for a Gentile to be all the way to the end of following the Law perfectly, they must simply not be too far on the other extreme. So non-Jews have to meet certain basic criteria to be part of the movement. Paul expects the return of Jesus to happen any day and so it is pressing that people make preparations. This might explain why he compromises because he feels that he needs to achieve as much as possible in a short time and requiring too much of the Gentiles could delay their conversion.
The case of Timothy may be explained using this model of a sliding scale. Timothy may have had such great faith that moving farther down the scale did not present much of a challenge to him and so Paul suggested it in order to make Timothy more prepared. Another option is that Jews are still bound by the covenant while Gentiles are not bound in the same explicit way. In this case Timothy’s Jewish heritage might have justified Paul’s decision to have him circumcised. A third option is noted by the CSB, Timothy was circumcised simply to make him more acceptable to Jews and thus to get more Jewish converts.
One can read Acts 15:1-16:6 as indicating Paul’s desire to get as many Gentile converts as possible without much trouble. He, after all, argues for their inclusion and doesn’t think they need to be circumcised. This seems consistent with the reading of Galatians where Paul is trying to maximize the number of converts possible, no matter what other differences there are.
If I am correct about the sliding scale then it would seem that Paul’s terms for accepting non-Jews are not stringent enough. Paul thought Jesus’ return was imminent and so a compromised position was acceptable. Since we now know that Jesus’ return has not yet happened it may be the case that all Gentiles should have been held to a higher standard.