1 Corinthians 9:21
To them that are without law, as without law, (being not without law to God, but under the law to Christ,) that I might gain them that are without law.
Note 9 at 1Co 9:21: To the nonreligious, Paul didn't act religious. It would have caused them to reject the message because of the messenger. Today our Christian cliches and mannerisms are, at best, meaningless and, sometimes, offensive to nonbelievers. Paul would have related to them as much as he could so that he could share the Gospel with them. Paul was not advocating becoming like the world, but he was advocating not trying to make the world become like us before they hear the Gospel. We have to catch the fish before we clean them.
Note 10 at 1Co 9:21: A New Testament believer is not obligated to fulfill the Old Testament Law for justification (see notes 3 and 4 at Ro 3:19). Therefore, Paul referred to not being under the Law (1Co 9:20), yet here, he said he was under the law to Christ. There are two ways to understand this.
First, Christians are not under the O.T. Law but under the N.T. law of Christ, which is to love God with all their hearts and love others as themselves (Mt 22:37-39, Mr 12:30-31, Ro 13:9-10, and 1Jo 4:21). If believers walked in this law of Christ perfectly, they would fulfill the righteousness of the O.T. Law. "Love worketh no ill to his neighbour: therefore love is the fulfilling of the law" (Ro 13:10).
Second, N.T. believers do not discard the O.T. Law; they just cease to try to fulfill it as a requirement for salvation. This is exactly what the Apostle John was referring to in 1Jo 2:7-8. In 1Jo 2:7, John said he wasn't writing a new commandment. It was the same commandment that they had heard from the beginning, referring to the O.T. scriptures. Then, in 1Jo 2:8, he said it was a new commandment--new in the sense that the holiness the Law dictated now comes as a fruit, not a root, of salvation.
So, Paul was not wrong to say in 1Co 9:20 that he was not under the jurisdiction of the O.T. Law, and he was not wrong in this verse to say that he was under the new law of Christ.