That's something I've always wanted to see. Basically, unless you have an Avengers membership to wash the stigma of your powers away in the public consciousness, it seems like these anti-mutant bigots would just lump everyone with powers under the "muties" label. Bigots aren't generally known for their keen understanding of scientific facts like exactly what genetic marker makes a mutant different from some kid who got bitten by a radioactive lemur.
"M-Day? What's M-Day? There are still tons of those filthy muties running around! Kids with powers are coming out of the woodwork! What now? The f*** is an 'X-factor gene'? If the kid can shoot lasers out of his butt, he's a goddamn filthy mutie!"
Well, I mean, that still basically happens. Most people in Marvel assume Spider-Man is a mutant. It was never brought up before his identity as Banner was revealed but it wouldn't surprise me if people assumed The Hulk was a mutant, seeing as how nobody new where he came from for years until Ross found out that Bruce was The Hulk.
I mean, there isn't a stigma about being a superhero with artificial powers, which makes a lot of sense to me, but most superheroes in the Marvel universe who are beloved and have artificial powers are, like you said, members of either The Avengers or the Fantastic Four. Everyone else, at best, nobody really cares about if they don't outwardly hate them. And about half of the c-list superheroes in Marvel who don't have powers are mutants anyway.
I also think it's important to remember that racism and bigotry take a lot of different forms, not just overt hatred and fear.
Like, for example, assuming that a black guy wearing plain street clothes listening to his iPod is listen to hip hop, that's racist. Assuming a person of Irish descent drinks a lot is kind of racist. Assuming that any random guy on the street is a pervert who loves sports, or assuming that any random woman on the street is emotional and loves shopping, those are both sexist. Being a straight person and immediately assuming that a gay person of the same sex you just met is going to start hitting on you is homophobic, even if you don't voice it and the feeling soon passes. They're not in of themselves harmful or evil. They don't really matter at all. But they still come from a place of bigotry, even if it's in an incredibly minor way.
Similarly, someone might assume that several super heroes who aren't mutants are because they don't know their origin story. And they might think well of them overall, but still hold weird and kind of arbitrary assumptions about them or expectations of their behavior based on stereotypes or ignorant opinions.