Is it that humans
don't use money, or The Federation
doesn't use money? I have always (despite lack of anything definitive stated onscreen) thought of the UFP as the national-level government - the level of goverment that mints currency. The name itself suggests the UFP is a federal republic. It would not make sense for a nation to have money while one of its states/provinces did not.
Just because people aren't paid for their work (Jake's writing) does not mean that money/credits are not distributed some other way. Perhaps the UFP issues everyone a certain amount of credits as welfare, or perhaps work FOR the Federation is not paid, but private work is.