I always assumed there was no currency within Starfleet, not within Federation as a whole. Or if there isn't then UFP is a communist organization. After all Leningrad is still called like that.
My own problem with the "no money" pronouncement was that as grandiose as is sounds, it really doesn't carry a lot of specific meaning. Although we could talk about the existence of media of exchanges since the use of shells by hunter-gatherers to get goods from early towns and cities, the nature of money is far from consistent. It has a history that shows money, both as a measure and as a commodity in and of itself, changes over time. No banks, no currency speculation, no investments, no payments between governments: these things developed only recently. Indeed, a fundamental problem for much of human history was the insufficient supply of coinage for anything but the largest transactions. That's why Roman coins would still be in circulations as late as the 19th century. I would find it difficult to expect that money would play the same role today that it will in the future, and I certainly would not want to return to the financial world my father grew up in.
If there is any sense to be made of "no money," it has to come from Picard's takedown of Ralph Offenhouse, when Offenhouse expected that his wealth (if it still existed) would have empowered him above Picard. I don't remember that Picard says there is no money, but instead, he suggests that money doesn't carry the import it once had. I think he says that there is no need to accumulate things. That is removed from having or wanting things in particular, and Picard doesn't deny their existence. And although he doesn't say it, Picard suggests that he is more powerful because of his position, and money wouldn't change that.