They don't have money but they do have the classic authoritarian hierarchy of SciFi.
Want to travel the galaxy? You need a starship. How do you get a starship? Join the federation.
Picard retired to a grape farm in France. How did he get that perk? Can anyone have a grape farm in France?
SciFi has an inherent power imbalance between the fleet and grounders. This comes from the ability to move around and drop bombs on people. As much as they try to stay in a socialist paradise, they still have tons of incidents that end up being solved the starfleet way.
It's a quote from starship troopers, but the idea of "Service guarantees citizenship" is what draws fascists to SciFi. It's a tough problem to fix in fiction and most of the time it's overlooked because spaceships are cool on paper. They make great entertainment.
The reality is that serving in the federation usually would mean you've never been on a starship bridge. You're 20 levels down in a maintenance hold with no outside view. Nobody tells you shit and all you know is the ship is being fired at and you're fucking terrified.
Even if you can pull up an external view on your tablet (which is a massive security problem), you still don't have any control over the fight. Now you can watch torpedoes coming straight at you and realize the captain can't stop it, and you can't either..
Morale would be constantly in the toilet, and without a bigger reward than to explore strange new worlds you can't see from the hold, people would be constantly quitting.
In conclusion, I'm not saying that star trek is fascist. I'm just saying it hand waves away 90% of the problems with their alleged utopia and people like watching action packed SciFi adventures.
I have a whole separate rant about weapons like lasers that travel at the speed of light. In the real world most fights would happen across distances, with ships being undetectable against the blackness of space, until a beam comes out of nowhere and instantly destroys your ship. But because it's fiction you can ignore this.