The first question to ask is whether this remarkable testimony of Paul is something we should imitate, or is this just something that apostles did—or that missionaries do who must adapt to other cultures?
The answer comes from one of the clearest commentaries on these words that Paul himself wrote in the next chapter. Look at 1 Corinthians 10:31–11:1. Here the issue is exactly the same as in 9:19ff., namely, how to relate to Jews and Greeks so as to win them for Christ. He says,