I've always interpreted the "no money in the Federation" thing non-literally. I think there's still a financial and economic system operating in the background (otherwise this would be the most radical bit of world building Star Trek has ever done - and Star Trek's world building has never been particularly innovative), but it's just that "money" doesn't have the same primacy in people's lives as it does in the real world today.
I imagine there would be an electronic system of debits and credits (hence "credits" being the currency) moving around in the aether, with money in its physical form having entirely disappeared. Less "evolved" societies like the Ferengi would still use a form of cash (latinum), as would backward societies like 20th century Earth (hence Kirk saying "They're still using money" in The Voyage Home).
But even more than the term "money" being associated with physical currency (a concept that's increasingly being phased out even in the real world), to Federation citizens "money" would be associated with the archaic mindset of capitalism, greed and exploitation - the accumulation of financial wealth for its own sake. As opposed to 24th century people who (with just about all physical needs like health, food and shelter met by virtue of tech like replicators and advanced medicine), can focus on bettering themselves as a goal in its own right. So you might study medicine or law, not because it pays well, but because you're interested in that field. You might go for a promotion in your job, not because it pays better, but you seek the satisfaction of having more responsibility.