Re: WWYCD: Hero with "Questionable" Political Views
You should check out the Ultimates. In Volume 1, Banner gets pissed at Thor and goes into a rant about how Thor had a psychotic break when he was younger, and he just thinks he's Thor reborn. Banner claims that his powers come from something else entirely, I think it's being a mutant. Also, Defender doesn't believe in magic, despite the fact that he works with Witchcraft.
As for the question, it depends what the view is. If it wasn't something that could conceivably interfere with the character's hero work, then Dreadnought would let it go. If he thought it could go against the team's interests, he'd have a private chat with the other character. Of course, given the other characters in the party, that chat would probably accomplish nothing.