Since when are bigots logical? it isn't like they would have nice things to say about all the non-mutant heroes anyways.
But sometimes it's about more than that -- it's a more basic matter of universe inconsistency, especially where screen adaptations are concerned. I recently rewatched all three X-Men animated series on Netflix, along with the series that two of them nominally shared continuity with; the '90s FOX
X-Men had a couple of crossover appearances in the contemporaneous
Spider-Man series, and
Wolverine and the X-Men was nominally in continuity with
The Avengers: Earth's Mightiest Heroes. But they were awkward fits. In many episodes of the original
X-Men series, anyone who displayed superpowers was automatically assumed by spectators to be a mutant. For instance, when Apocalypse made his first public appearance, people yelled that a mutant was attacking. But in
Spider-Man, people were displaying superpowers all the time, but the only time mutants were ever mentioned was in the X-Men crossover. And WatXM was set in a continuity where there was this fascistic government agency called the Mutant Response Division imposing a nationwide crackdown on mutants, but aside from a throwaway reference to the "Mardies" in one A:EMH episode, that pervasive witch-hunt mentality was completely missing.
Now, sure, in both cases that's because the X-Men shows came first and weren't designed to accommodate the other shows that were added to their continuities later. What you're proposing is the other way around, adding mutants to a universe about other Marvel characters. And sure, that could work, up to a point. But I think the reason I'm resistant to that is that I think the X-Men story works better if the whole mutant-rights issue is in a distinct reality, if you don't have to try to do a handwave to reconcile it with other superheroes' existence.
So sure, you could have mutants in
Agents of SHIELD to some extent, but it would have to be handled rather differently than it's handled in the X-Men movies. Mutants would have to be something that's still secret, since the world in the MCU is being portrayed as just recently catching on to the existence of superbeings. So they couldn't be as pervasive in society, they wouldn't be subject to widespread or institutionalized persecution, etc. It would be so different from the usual X-Men saga that it's questionable what the benefit would be. (The second animated series,
X-Men Evolution, kept mutants secret from the world until a bit over halfway through its run, and it didn't really get interesting until they were outed and the show could start dealing with the themes of intolerance and persecution.)
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.
Yeah, but by the same token, anyone could come into possession of a piece of advanced weapons technology, or be exposed to exotic radiation and change into a superpowered being, or find a magical or alien artifact, or undergo an experimental medical procedure, or train in a far-off land to master mystical forces, or whatever. There are many ways for "normal" people to get superpowers, which kind of negates the whole "mutants are superior" fear. It doesn't make much sense to fear that normal people will be supplanted by mutants who can shoot beams out of their eyes or exert superstrength or mentally transform reality when Iron Man can shoot beams out of his hands, the Thing can exert superstrength, and Dr. Strange can magically transform reality. Both subspecies come out about evenly matched. So that fear of mutants supplanting us, except in the long term by a demographic shift over generations, makes more sense in a continuity without other superbeings.
