Bounty Hunters wouldn't have allegiances and he does give them the information they ask for.
I don't remember them doing a character check on Han when he turned up in his tracked ship leading the Death Star straight to their hidden base.
Fett is in it for the money so he could have even helped get Lando into Jabba's palace as a sweetner (which gives the nod he gives Boussh a different meaning too). If you think about it Lando's disguise is bordering on the Clark Kent, especially with Boba Fett wandering around the palace.
By finding and delivering Han to Jabba he's proved himself as capable. When Kenner (or rather Palitoy in the UK) sold the action figure pre-ESB they played on his ambiguity (will he save the galaxy or destroy it....or something like that, Marvel used the same line on Luke).
Being a small vulnerable group I'd imagine the Rebels would take information from wherever than can get it (as long as they can check the accuracy).
They may be a small group compared to the Imperials but they seem large enough to have a few generals who didn't care that much about Han and saw dealing with someone like Fett as a necessary part of their intelligence gathering.
Having Fett in Jedi was a fan service so if he has to be there at least have him in character with what we have already seen of him and leave him as a loose end (everything is too tied up or assumed tied up in a pretty bow by the end of all the official versions).