The more I think of it, I don't think mutants would want to be identified as mutants but not all of them will be super heroes or super villains. In a modern western culture, what would the politically correct term for Mutant be?
Scientifically, humans with natural genetic alterations would be Homo sapiens sapiens if they can breed with, and produce fertile offspring from, Homo sapiens sapiens. If they can't, then they would be Homo sapiens deinde. (Deinde is Latin for next, if you're curious.)
Most people don't go by scientific names, however. The average individual instead refers to other individual(s) as he/she/them/we/us/you. There's also countless ways to refer to the gender identity of individuals, not all of which are politically correct, of course.
Laws already account for the generic case: person.
There's no reason not to keep using the term person to refer to both Homo sapiens sapiens and Homo sapiens deinde. Assuming, of course, the latter is legally a person...
Shadowrun's answer to this is Metahuman. As the wiki page explains, the word "metahumanity" can be used to refer either to humans (homo sapiens sapiens) and their mutated cousins, or to only the mutated races excluding humans. Assuming you want a linguistic distinction to be able to talk about mutants without using the word mutant, you'll want to go with the latter case.
You could come up with a variety of similar words that perform the same purpose ("novohuman" for example), but I think metahuman rolls off the tongue better, and meta is a commonly used word in its own right these days, so you'll probably have to do less constant explaining of what you're talking about.
Homo superior is a possibility, if the mutations provide advantages.
If you want something that isn't going to be threatening to non mutants (recommended) then Homo mutandis "The Changed Man" would be better.
Building off of that, Changed might be a good start.
If you look at the history of some of the current politically correct terms, it's kind of a moving target. For the "Intellectual and Developmental Disabled", past PC terms were Cretin, Idiot, Imbecile, Moron, Feeble-minded, Retarded, and others. All these entered the language, and then became insults, which forced a name change.
As you might expect, there are lots of slurs behind most of the links in this answer.
Given the frequency with which marginalized groups reappropriate slurs, I think it's likely that at least some mutants would call themselves mutants, around each other and maybe also around genotypical people. I think it's equally likely that many hypervariant and hyperabled people would be wary of reappropriation efforts. I expect clinical terms taking on lives of their own, names originating as slang within charm communities, names constructed to emphasize Varied people's friendliness and respectability, names reflecting the gallows humor of the freaks and the Cursed, insipid Latinate terms intended to convey neutrality toward parahumans but crawling with fear and revulsion, and hopefully also enthusiastic co-opting of classic monster movies.
The most politically correct one would be the one selected by that minority group. In all cases of vernacular syntax, there's a wave of names that will be attributed to a certain group or groups. It follows a fairly recurring progression:
Corrected Exterior Label
Internally Accepted label
For example, Followers of Jesus were originally all considered
1) Jews in a cult, then were called
2) 'Christians', which translates to "Little Saviors" or "little Christs" by Greeks and Romans, then Romans separated
3) Jesus-Followers from Jews, calling them Followers of the Way, and finally
4) They incorporate the name "Christian" for themselves.
You can see that with other groups as well - 1) Deaf 2) Dumb 3)Hearing Impaired, then they agree on the label 4) "deaf". Something similar happened with people unable to walk (although it took effect over a LONG period of time) 1) Handicapped 2) Lame/Cripple 3) Disabled 4) Impaired.
In your story, there should be a similar progression. For example, if you're in a X-men, Inhuman, Chronicle or similar style of world, that can be a minor plot element. Something like a: 1) Biodynamic 2) Mutant 3) Genetically Different 4) Biodyn.