I think it has more to do with the fact that at any point a pre-teen can just grow powers randomly and with no warning, which is frightening.
Plus I point you all to spider-man, nobody like him and when they do they all quickly go back to hating him again. So it's not just the mutants people don't like.
Spider-man had a decade long smear campaign run against him by JJJ.
Well, the main fear is that humans can become mutants at puberty without any wild exposure/triggers. "What if my son/daughter is suddenly different?" The Fantastic Four went to space and got hit by a once-in-a-lifetime energy shower, Captain America had a top secret drug, Iron Man invented a suit of armor, etc. Mutants are feared because anyone can become one at any moment. I'll agree it's still a bit muddy simply because we're dealing with cape comics and 70 years of continuity, but the general idea is that anyone can become a mutant in the blink of an eye, living an ordinary life.
I hate to appear to be spamming this thread, but I enjoy discussing X-Men and mutant politics :/
I suppose I see your point. But due to said continuity, those once in a lifetime accidents happen pretty often. Look at all the current and former non-mutant teen heroes.