In a world where superheroes have been around for decades, why would people be so against mutants? The X-Men stories work better in a world where they are alone, and the 007 films work better when each Bond is in his own universe.

I agree in general with what you are saying as far as the movies but as an X-Men fan I will answer the second part. Mutants are a minority group and what is one thing we know about racism/misogyny/bigotry/prejudice? It makes no sense. It makes no sense that a person can hate all black people but root for the black guys on his favorite football team. It makes no sense that someone can hate immigrants but love their nanny Maria and gardener Juan. It makes no sense that some can say "I am not anti-gay but pro traditional marriage". It makes no sense that South Carolina is worried about Sharia Law. That shit is completely illogical.

You are right. It makes no sense that people would root for the Avengers but hate the X-Men except it does make sense from a real world perspective. Captain America, Hulk, and Spider-Man are humans. They represent humanity. They are the peoples champions. Mutants are the other. They represent a threat to humanity as a species that the Avengers do not. Odds are you aren't going to lose your job to Iron Man, but you might to a mutant. You probably don't worry about your daughter dating Hawkeye, but you'll be damned if she dates a Mutie. You are suspicious of that green kid down the street. You certainly don't like that your little Suzy goes to school with those gene-freaks.

So even though people may like the X-Men because they are superheroes. The X-Men are "the good ones". Mutants are hated because people fear them, they are a threat. It isn't about them having powers, it is about what people think they represent. It is genius that they would love The Avengers and hate the X-Men.