Actually the Maquis hate the Federation NOT the Klingon Empire as the Klingons actually supported the Maquis and supplied them. The Maquis do not have beef with Klingons, quite opposite. They would more likely see them as allies against the Federation who they see as their true enemies.
So yeah, get it into your head not everyone likes the Federation Collective and there are Federation Separatists.
The Maquis were fighting the Cardassians, so yeah, I'd expect them to get help from anyone and everyone that would benefit from that. But, if they were put into STO the big enemy would be the Klingon Empire. Mostly because it would likely be the Klingon Empire that would be occupying Fed worlds. And while I agree that not everyone likes the federation and are right to feel that way, it was never a case of the Maquis hating the federation as an enemy. I suggest you watch some of DS9 or peruse Memory Alpha to get a bit more insight into the Maquis.