I always understood Star Trek's cashless economy being based (and dependent) of/off replicator technology. Of course, this is only true starting with The Next Generation. In The Original Series they were still talking about Federation Credits, etc. Back to replicators: Once you're able to create things with pretty much no effort, they're losing their worth. You could probably compare this to books a few hundred years ago and nowadays: Back then someone might have spent months or years copying the Bible. Today you'll need at most a few clicks and some energy.
In Star Trek you've got a similar promise, just for more things other than just books: If you're able to copy a cake or even a car with little to no energy or time consumed, it will be rather cheap or cost next to nothing. As seen in The Next Generation, replicator technology seems to be readily available pretty much anywhere. It's often even part of some kind of emergency plans or temporary shelter used for evacuated people.
But back to the initial question: I could imagine that you won't need money, even outside Starfleet, as long as there is replicator tech available. As for interaction with other species or races not having such technology (remember prime directive and stuff) they'd probably provide fixed amount of currency to diplomats or people working there (obtained by trade or services), similar to how things like this can work in modern day as well. For example, if you're working overseas for your company for some time, it's more than likely you'll get money by your company to be used there. You don't necessarily have to have your own money (at least not for everything; again: remember the replicators).
One could argue there's still energy to be paid for. I'd agree, but considering the sheer amounts of energy required for a warp engine (despite considering Einstein & Co being wrong), I imagine this would be next to neglectable using fusion and/or matter/antimatter plants.
As for Latinum: I never liked the whole idea around this, but the authors clearly lacked some money aspect when handling some events and species (like the Ferengi), so they had to add something you can't just copy in a replicator without making the currency (once again) obsolete.
But overall, there's still some plot hole I never got around finding a real explanation: In the Star Trek universe is it really like everyone being an "oh I work very hard every day just to make the world a bit better, yay!"? The different series often feature characters who might get thrown out of Starfleet and the like, and pretty much all of them act like that would be the end of the world. Why is that? With no money needed, you could essentially take some time for yourself whenever you want, even if that would cost you your job. It just doesn't make sense overall.
Also, as an additional note, I've once read a very nice article on cracked.com also mentioning how we've already achieved "Star Trek's Utopia" at least partially. Just read reason #5. This pretty much explains how replicators made money obsolete and how we already could have something like that (in a limited way).