In a broad sense, I think that all Marvel heroes have been hated and feared in a way, mutant or not. It's one of the defining characteristics of a Marvel superhero. There's always this sense that they're a menace and can't be controlled. Thus, there is the distrust. Spider-Man, the Hulk, Namor, Ghost Rider are some of the "heroes" that come off the top of my head. But there have been instances when Captain America, Iron Man, and the Fantastic Four have been deemed threats and menaces.
But okay, that's stretching things. Yes, all MU heroes have encountered fears, but the X-Men have gotten it WAAAAYYY worse. Straight up prejudice and discrimination, the likes of which Captain America hasn't encountered before. I think of the reasons MU superhumans never encountered discrimination was because humans saw them as being "one of their own." As amazing as Captain America was, he still sided with humans and fought for them. Mutants, on the other hand, were seen as the other and, as already been pointed out, were the next stage of evolution. Busiek's and Ross' "Marvels" touched on that a lot, how humans were afraid that they would be enslaved by mutants and killed by them all. Phil Sheldon confronted that prejudice starkly when he finds Maggie, a mutant girl hiding in his basement:
Compound that with Magneto and his Brotherhood constantly saying that mutants were superior to humans and deserved to be enslaved, and well, that's how you have that attitude.