My theory as to why we’ve never heard of Mutants up to this point despite them seemingly always existing is that every Mutant with mental manipulation powers got together to make everyone on Earth forget about the existence of Mutants in order to escape oppression.
Now, of course, this presents problems of its own because, whether it’s successful at it or not, Mutants are supposed to be an allegory for real marginalized groups and, without that, the plot’s kinda been lost. To that, I say, have the main antagonist of the first X-Men movie be a Mutant conspiracy theorist whose obsession with (the idea of) Mutants and desire to be right leads to the reversal of the mindwipe, thus restoring the hatred of Mutantkind and even making it worse because people would now know what happened