They use replicator rations as currency and exchange them for goods and services. In a world that frequently says that society has progressed beyond the need for money. As soon as things become scarce they start using a market again. Thus, the lack of scarcity in the Federation precludes the concept of an economy at all.

And yeah Starfleet ships are always militaristic, but people can choose to leave if that's still an option. I believe this was why RDM left the writing team, but it never seemed right that Janeway just appointed herself dictator when this ship was potentially in for a multi-generation journey. BSG handled that sort of thing much better.