Note 3 at Ac 16:3: Paul had already argued before the council in Jerusalem that it was not necessary for the Gentiles to be circumcised to be born again (see note 2 at Ac 15:1). The apostles and elders had agreed with Paul and written letters to support that position (Ac 15:23). So why then did Paul circumcise Timothy "because of the Jews"? It looks like Paul compromised after he had already won the victory.

It is certain that Paul did not circumcise Timothy as a work of the Law for the purpose of justification. That would have been against everything he taught (Ga 5:2-4). It is possible that he did it as a matter of not giving offense; that would be consistent with his teaching (1Co 8:9 and 13). When confronted by the legalistic Jews about Titus' circumcision, Paul refused to compromise on this issue (Ga 2:3-5). Therefore, it is certain that the circumcision of Timothy was not a reversal of his position on God's grace.