Note 3 at Acts 16:3: Paul had already argued before the council in Jerusalem that it was not necessary for the Gentiles to become circumcised to be born-again (see note 2 at Acts 15:1, p. ???). The apostles and elders had agreed with Paul and written letters to support that position (Acts 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 (Gal. 5:2-4). It is possible that he did it as a matter of not giving offense which would be consistent with his teaching (1 Cor. 8:9, 13). When confronted by the legalistic Jews about Titus' circumcision (Gal. 2:3-4), Paul refused to compromise on this issue. Therefore, it is certain that the circumcision of Timothy was not a reversal of his position on God's grace.