There's nothing self-contradictory about those things in themselves, obviously. It's the fact that there are other things in canon which, y'know, contradict the implied or express use of money which are contradictory. Thus rendering canon self-contradictory on this issue.
And by "other things" you're referring to that single line of dialog in First Contact? There was never any consideration of there being no money during the production of TOS in the 1960's. And I can't recall ST: Enterprise discussing the subject one way or the other. Nor do I believe Voyager ever directly brought up the subject of no money.
During the creation of TNG, Gene Roddenberry express a vague idea of there being no money in the 24th century. But when pressed by the shows writers, he was unable to explain what he meant in even the most simplest of terms. The writers themselves lived in a society with money, whether deliberately or unintentionally, the existence of money in the 24th century worked it's way into the scripts.
If you say that there is no money whatsoever in the 22nd, 23rd, 24th centuries, you basically building that supposition on a single clear overt statement. Which flies in the face of dozens and dozens of examples of a more conventional financial system.
It not like it is a fifty fifty mix of yes money and no money examples. Your isolated evidence does not make the five series' position on money "contradictory."
The idea was expressed more than once and you know that, T'G. Star Trek IV for example:
Gillian: "Don't tell me, they don't use money in the 23rd century?"
Kirk: "Well, we don't."
And we didn't see Gillian offering to pay that pizza and beer with cash. She may have been pulling out her Visa or MasterCharge, i.e. using credit not cash. And the moneyless concept was repeated on Star Trek DS9:
Simple logic is all that you need. It seems Roddenberry's intent was to go with the moneyless future scenario as sci-fi writer Iain Banks was already doing at that time. Otherwise, why would Star Trek bother to bring it up not once but multiple times?
Of course, many different writers worked on the show and like you indicated, they come from our monetized era, so naturally they may have had some difficulty negotiating the moneyless society concept. And with the time constraints of television productions they wouldn't have had much time to explore the concept. Maybe they should've read more Iain Banks or study history a bit more.
"Bread, meat, oil, wine, and certain other products were distributed gratis from the community center where the peasants deposited their products....
'Are you not afraid,' I asked, 'that unlimited quantities of free wine will lead to excessive drinking?'
'By no means. No one gets drunk here. We have been living under this system for a year, and everyone is satisfied....'"
-- The Anarchist Collectives by Sam Dolgoff.
Kirk didn't have to pay a thing for Uhura's drinks.