Jamieson, Fausset and Brown on 1 Corinthians 9:20

20. I became as a Jew--in things not defined by the law, but by Jewish usage. Not Judaizing in essentials, but in matters where there was no compromise of principle (compare Ac 16:3; 21:20-26); an undesigned coincidence between the history and the Epistle, and so a sure proof of genuineness.

to them that are under the law, as under the law--in things defined by the law; such as ceremonies not then repugnant to Christianity. Perhaps the reason for distinguishing this class from the former is that Paul himself belonged nationally to "the Jews," but did not in creed belong to the class of "them that are under the law." This view is confirmed by the reading inserted here by the oldest manuscripts, versions, and Fathers, "not being (that is, parenthetically, 'not that I am') myself under the law."