As a group of individuals who have superhuman powers living in a world filled with superheroes...then yes, they fit. But the idea of these superhuman individuals living in genetic prejudice when the world sees these kinda acts all the time doesn't fit.
I think the distinction is one of source. I think, even in a world populated by superheroics, genetic prejudice still strongly makes sense.
I think, for one, the very idea of superpowers is something that's underestimated. Honestly, the thought of superhumans is scary, far scarier than we usually see played out in comic book panels. Superhumans are essentially walking, talking, thinking WMD's. But I think there's a clear enough distinction in the origin behind mutants rather than other superhumans to make their central metaphor still relevant even in the context of a superhero universe.
I think the
spontaneity of mutation makes it a beast in its own right. Sure, superhumans in general represent a scary new front on the pervasive front of the global arms race, but in terms of conventional superheroes, they still follow the conventional scale of the arms race. It's still an essentially capitalist practice. The majority of "typical" superhumans achieve their powers through government or corporate projects. There is a level of accountability. There are contracts signed and there's either accountability on the part of their obligations to the government, or accountability insofar as the government can label them as having volunteered themselves for illegal experimentation or as willing enemy combatants. Those that aren't typically have external sources for their powers that can be confiscated or used to contract the individual to the government. And, while it's scary that these guys might be running around, it still fits the typical ideology of arms escalation. America will always have the best weapons because they have the resources and the money. It's a terror, but it's essentially just an escalation of the same terror we've lived through for fifty years, and so it's a terror we've long grown accustomed to. The powers themselves are typically, for those who carry them, a means to an end for a profession that makes them clearly definable as "friend or foe". They acquire their powers as a means to become a vigilante, a criminal, a soldier, or what-have-you.
Mutants, OTOH, are purely egalitarian. They're unpredictable. There is no way of knowing who will manifest powers or how they'll manifest them, no trail to follow. And the more worrisome part is that you can't prosecute them for the fact that they have powers. It's an intrinsic part of them. With Captain America you can say pretty easily that, since he subjected his body to military experimentation, that said powers are under contract to the government, or that since any number of Spider-Man villains subjected themselves to illegal experimental treatments, that their very bodies are in violation of national security. But with mutants, you come under fundamental rights based violations. If you accept that mutants are a natural evolutionary process you raise any number of theological and philosophical questions about the nature of man. You raise any number of questions about cultural, species and racial identity. Superheroes are just humans who have been souped up. Mutants are something else entirely. I honestly think there are just as many interesting stories that are stronger in a shared universe as there are where mutants are the only flavor.
I actually quite like what's been done with the X-Men, despite never having been a huge fan of that whole little corner of the universe. The idea of a population of superhumans who's origins and motivations are in contrast to the typical "superhero" and who have made their own little social and political identity is a strong one, and one that complements the rest of the universe well. I like them being sort of cordoned off in their own private part of the universe and separated from the whole "OMG NOTHING HAPPENS OUTSIDE OF NEW YORK CITY!" focus of the rest of Marvel, but I see no problem at all with them sharing a universe and crossing over with other characters.
Then again, I hold a pretty ambivalent stance towards continuity. I feel it's best to let a book and character take liberties an exist basically in its own pocket for the most part, but let it converge into crossover and mingle with other parts of the universe when it bests benefits said character or book. I think
Thor was a good example of how this works well and how it fails. When JMS was writing the book, it was clearly settled in the mainstream universe but the characters and setting were well compartmentalized so that they didn't touch other aspects of the universe except when it clearly benefited the story.
Siege is an example of where it doesn't work, where you force this setting to dramatically mingle with the rest of the universe and nobody benefits except the meta-setting. In essence, it becomes an excuse for Bendis to bring in his "Avengers" toys and have them blow up the awesome "Thor Mega-Castle Playset". It's like when I used to have the Teenage Mutant Ninja Turtles raid Castle Grayskull. The Turtles look like wicked badasses doing it, but the He-Man guys get the shaft, and nobody really benefits or grows in the end. The characters of Thor's setting become cast-away pieces in a big event set-piece where they're barely bit players, all for the sake of some sort of greater continuity. X-Men, conversely, is doing a pretty great job ATM of remaining independent thematically and setting-wise yet still being firmly embedded in the overall tapestry of continuity.