What evidence is there to discuss the issue of Paul and Culture? Many turn first to Acts 17, or questions of education. I am not opposed to this, but my concern at this point is what we can find from his letters.

I’m rushing off to a trip to Europe with my family (so this isn’t comprehensive), but these are some things that speak for Paul’s positive and negative engagement with culture.

I have become all things to all people (1 Cor 9).
The household codes in Colossians and Ephesians are often noted a accommodation to culture.
He allows people to eat with others, even if offered to an idol (1 Cor 9-10)
In distinction to Hebrews 11.13 and 1 Peter 2.11, I can’t think of any time where Paul speaks of Christians as being aliens. However, the longing in Rom 8/2 Cor 5 may be noted, but that’s more soteriological than cultural.
Paul worked, and thus engaged in economic exchange.

His use of the world, this age, the god of this age
He definitely challenges the ethics and religion of the G-R culture (cf. Rom 1.18-32)
food interaction
Anti-imperial language

The list could be fuller, but no time now. What would you add?