Following are a few ways to take this trope.
- Someone powerful has a vested interest in this persecution and is disseminating propaganda. A church preying off of its worshippers' prejudices, an iron-rich nation making money off the sale of weaponry (or, even better, a nation replete cold iron/silver/adamantine/..., a material which just happens to be the "mutants'" weakness), a powerful demagogue seeking to unite "pure" humans/demi-humans--these all have literary (and real-world, sadly) antecedents.
- It's known that there is some temptation concomitant to becoming a mutant. Not all mutants are bad, but one hears enough stories about the bad ones that fearful/superstitious/bigoted commoners have generalized their trepidation to all mutants. Close to the reasons adduced in "X-Men," although that, too, has a healthy dose of the above machinations.
- Simple novelty might play a role. Half-orcs, sorcerers, and witches may have been around long enough to have achieved (ostensible) equality, but mutants are a newer phenomenon. Once again, in real life, marginalized groups are subject to disparate amounts of suspicion and abuse, and what was regarded without rancor yesterday may now be the despised minority du jour. Real-World Trigger Warning:Examples here would be the rise of Islamophobia or the rampant burning of black churches in the contemporary U.S.: these prejudices have been around for a long time, but they recrudesce and gain lethal force when it suits the caprice of the white majority.
Well, that got grim, but I hope that the post provided you with some ideas nonetheless :).