It's a fairly common fan question, and one that is set pretty firmly in the grand tradition of the Marvel Universe:
Why are mutants so feared and hated but the Avengers and the Fantastic Four
get respect and celebrity status?
It's an understandable question really - what really separates one clan of spandex-clad "freaks" from another? But there is some underpinning behind the disparity; let's look at it.
The first thing to keep in mind is that in the context of the Marvel Universe, the Fantastic Four and the Avengers are just barely tolerated for existing - and let's not forget that these groups include Reed "Smartest human in history" Richards, and Captain-I-punched-goddamn-Hitler-America, among various other rich philanthropists, world-renowned scientists, and other luminaries. Nevermind that both the FF and Avengers spend a great deal of time on Public Relations and philanthropy - whether it's Reed announcing some new scientific breakthrough, the Maria Stark Foundation doing some major charity donation, or a press conference where Captain America and Iron Man explain that Thor totalling that aircraft carrier was seriously the only way to stop Ultron, etc. In contrast, the X-Men show up, cause some damage, and leave without saying a word or leaving it up to SHIELD or someone else to explain their actions for them. Not the best way to win hearts and minds, to use the cliche.
What is unique about the fear of mutants is the level of uncertainty. I mean, yes, there's a chance that a given ordinary individual could get hit with gamma rays or accidentally end up in a cybernetic battle suit or encounter some mystical doohickey that turns you into a monster, but that's the exception. By contrast, being a mutant is a more common occurence, one that has nothing to do with any choices or any kind of human error - it's genetics. This is compounded by the "fear of replacement" (i.e. "our replacement as a species have arrived, and they are nearly godlike in their power") and the inconvienence that most mutant powers manifest during adolescence - not exactly a great time to be practicing impulse control. Just imagine the kind of havoc that would have been wreaked by your average school-shooting kid with the powers of say Colossus or Gambit. Not a pretty sight at all.
Now, all this said, it's rare that we see anything other than the monoculture of bigotry from the MU, and that's equally stupid and offensive. I can't imagine what the Transhumanist movement would be like there, but one could easily imagine it as more vital and with more than a few proponents in the mutant and superhuman communities. And here's an idea that will never, ever, EVER get an X-Men comic out on the shelves: imagine a test developed to detect the X-gene in utero, and then imagine the entire Abortion debate turned on its head.