Since when are bigots logical? it isn't like they would have nice things to say about all the non-mutant heroes anyways. Thor is a foreigner who claims to be a god. Hulk occasionally destroys city blocks. Every time any of them have a fight they risk destroying neighborhoods.
The fear of the Mutants comes from the fact that anyone's child might be one, that they're replacing humanity. That they are superior and might one day realize it. And, rightfully so, some teenager who can't keep his boner down in class might one day wake up with lasers shooting out of his eyes, or mutate into a living bomb or a plague, or rip apart reality around him. Combine that with how many mutants are freakish looking and DON'T have powers, and you have a lot of easy targets and a recipe for people putting the blame on those freaks out there, rather than those nice Avenger gentlemen.
The comics don't always portray it well, but comics do a lot of things badly.
Plus, it gives them another option for super-powered threats other than "mad scientist" and "military experiment", which would be handy assuming they aren't going to bring in the Skrulls or other Asgardians any time soon. Spider-Man's rogues gallery makes for some pretty formulaic movies because of this.