How does the Federation's Starfleet members pay for stuff from non-federation members?

(Pay-)in-kind

The Federation still conducts trade with non-federation worlds, and would procure foreign currency through that.
Likely similar to the way that East Germany procured western currencies, since its own currency could not be exchanged directly.
I would imagine that Starfleet members in such situations would get an allowance of gold-pressed Latinum.

It depends. Which non-Federation members, and for what?

The Federation still has credits. But many things in high-technology places don’t cost anything, because they’re so easily produced. Think of water from a water fountain, but many other common things being similarly free, because there is so much energy and replication technology available.

Latinum.

They use Apple Pay. Works anywhere. (By Stardate 1312.4, Apple was running the galactic banking system)

They barter.