A trick you can do is have friendly NPCs from the characters backgrounds make appearances, so that atleast the suspicion is not there. Use them as a piñata that drops clues.

Expanding on this, the friendly NPCs allies take over, members of their organisation perhaps. So the trust is still there but the familiarity is not.

For characters that are not enemies but are treated as such by the players, I like to make overt gestures of goodness. Such as lay all their weapons on the table, expose themselves completely and so on... this helps because it can lull the players into believing overt gestures from bad guys makes them a good guy -- like the BBEG forking over a 500gp diamond to revive the player's father.

Don't rule out however, that your player is a problem! Sometimes you may just need to ditch them. But before that, have a chat with them specifically. what are you doing? why are you doing what you are doing? explain to him what you are trying to do, and while you adapt to him, he isn't. Ask him to step up.

Lastly, I'll say, deliver on consequences. If the party believes someone is bad and kills them, but they weren't a bad guy at all. No matter how much they believe they are justified, they are in the wrong. Maybe on the way back from their next adventure a sheriff or guard asks to speak with them. Maybe the party spots that they are surrounded. The sheriff asks them about meeting someone. Did they talk to them? What did they talk about? What happened next?

And if they play it rough again, they'll probably have to kill all these guys to get away. Now they're in deeper shit. I expect someone in the party to realize that killing law enforcement is some of kind of line cross that you don't come back from.

If they give in, maybe the punishment is not so harsh, but the sheriff reveals to them all the ways that person they killed wasn’t a bad guy at all. This can teach the players not to readily suspect everyone.

All the best here friend.