Perhaps Sybok thought that only a Federation starship would be able to get his mission completed. Either because they'd be easier to control enough to get onto the ship to get it heading towards the Center of the Galaxy. Or he thought it would be the only power with a ship fast enough or strong enough to get through the Galactic Barrier or whatever he expected to encounter.
Again, when one actually picks apart the logic of this movie, it's clear that Sybok didn't even need to stage this kidnapping in order to get a ship. Klaa's POS bird-of-prey made it to the "center of the galaxy" just as easily as the Enterprise. Clearly Sybok was resourceful enough that he could have gotten any ship and any crew to take him where he wanted to go. He probably could have just flown there himself.
Imagine if STV's editors had simply eliminated the whole Sybok/ShaKaRee/God nonsense and actually focused on the kidnapping/hostage situation as the main plot of this film, with three opposing governments trying to rescue their respective ambassadors in their own ways, and the "villain" of the movie was an actual sadistic villain instead of a misled, prone-to-unnecessary-smiling-and-laughing, heretofore-unknown member of the Spock family.