It's not just mutants. If you can get bitten by a damn spider and turn into a superhero mutants are not your problem -- anyone
could get powers by that point, and that's when you say "oh hey, wait a minute, what the fuck are we gonna do about this?"
And Civil War was horrible, but mainly because superhero registration is pretty damn sensible and they had Captain America be really fucking stupid about it. If you live in the U.S. you have the right to own firearms, but you don't get to keep it a freakin' secret -- even the NRA is on board with background checks and such. There's no earthly reason possession of superpowers should be any different. If you are a freakin' superhuman the authorities damn well have a right to know about it, because you're a freakin' superhuman.
This isn't exactly rocket science.
Well Spidey is hated and feared, after all.
You're sort of sliding past my point, though. Mutants are scary because they can appear without warning. It both offends the American ideal of equality of opportunity (how are we equal if, when I hit puberty, I can move objects with my mind for no reason other than genetics?) and incites the american fear and intolerance of that which is different. I mean, one of the main members of the X-Men team has a power that's uncontrollable and incredibly dangerous and must be controlled artificially.
This guy has been continuously blasting energy beams from his eyes that can level buildings since he was a teenager and he can't switch it off
. Just as I said, you, the average Marvel citizen, now have to fear that when your daughter goes to school one of her classmates will explode and level the building, start emitting radiation that gives her cancer, have aliens from the Negative Zone start crawling out of his asshole... or maybe he'll develop X-Ray vision and look at her naked for his spank bank, or develop psychic powers and manipulate her into deviant sexual acts.
Or maybe she'll do one of those things, and you can't
. Or she gets a fever and five days later she's a leather lizard monster and kills herself.
People are unreasonably paranoid about minorities being around their kids now, imagine if the minorities could fly or teleport or breathe fire.
Other superheroes aren't as terrifying to the people because they're reproducible even if they're unique. I could put on an iron man suit or get bitten by a radioactive spider or be injected with super soldier serum or absorb gamma rays.
Now, you might say there are obvious reasons that isn't true (even in universe gamma radiation kills most people, only a very select few get powers from it) but that's how Americans think. That's why you can bamboozle people who make $30k a year to vote for taxes increases for themselves to preserve the riches of the wealthy: The fallacious believe that well, if the right obscenely unlikely things happen, that could be me!
I'm coming back around to my point: The X-Men are getting to be like Star Trek, hitting the same tired old noncontroversial points (we should tolerate people who are different! No, really?) instead of using the text of the books to say something about American culture.
Marvel comics used to be at the forefront of social movements and counterculture, now they're dragged behind, patting themselves on the back for being progressive. They're running on the fumes of their own hype.
Edit: Now that I think about it, the absolute worst thing Marvel did for mutants is make them all adults. If I was EIC I'd order that the X-Men end with all of the remaining mutants getting together to discuss mutancy when suddenly Cylops's head explodes and kills them all.
Then bam, reboot the concept of mutation with an entire new generation of mutants who are all under eighteen.