In Fact He Puts Everything Into His Work Of Winning Men For Christ (9:19-26)
'For though I was free from all men, I brought myself under bondage to all, that I might gain the more. And to the Jews I became as a Jew, that I might gain Jews. To them who are under the law, as under the law, not being myself under the law, that I might gain those who are under the law. To those who are without law, as without law, not being without law to God, but under law to Christ, that I might gain those who are without law.'
For it is he who is the debtor (Romans 1:14). He is a debtor to all, a slave to all. He is a free man, indeed a Roman citizen, a man with great privileges, but he deliberately makes himself a slave and in bondage to all men. And he is ready to shape his life in any way necessary in order to gain as many as possible for Christ. That is all that matters to him. The fact that he is free from all because he earns his own way does not affect his dedication to his task. It rather accentuates it.
To the Jews he becomes as a Jew so as to win them for Christ. To those who are under the Law (here possibly widening the scope to include God-fearers who meticulously followed the Law, although not Jews) he becomes as under the Law, just as Jesus had done previously when He had observed all the tenets of the Pharisees, while not Himself being a Pharisee. Even though he is not actually under the Law, he will observe it scrupulously before them, and when he is with them. He will do anything not to put them off as long as it does not contradict the Gospel.
And to those not subject to the Law he becomes as one without law, as one who lives under the principles they live by, although he stresses that that does not mean that he becomes wild, or careless, or lawless. He is not without law to God. He recognises the inward law established by conscience (Romans 2:14-15). And he is under law to Christ. he acknowledges his responsibility to follow Christ's teachings and Christ's example. He would not, for example, eat things openly seen as sacrificed to idols in a pagan temple. He is still under God's general law as revealed by conscience, and under Christ's principles of life. But while remaining in line with Christ's teaching he abstains from involving himself while among them with those things that would put off those not under the law, the ritual teaching, the food laws, the washings, the laws on cleanness, and any other things that really only affect the Jews. And his purpose is so that he might gain those who are without the law for Christ.
The point here is about religious behaviour not moral behaviour. He does not mean that he will literally do anything, whether sinful or not, to win men. He means that he will not allow particular religious ordinances to get in the way of the acceptability of his message. If it will help he will perform them, if it will not help he will avoid them.