I should begin by admitting that there is a considerable amount of speculation involved in this answer. However, this speculation, as far as I can see, is consistent with the storylines from the Marvel Universe.
For the most part, other superheroes became superhuman, often because of an accident or some other unforeseen events. For example, Spider-man was a normal person until he was bitten by a radioactive spider. The Hulk was a normal person until he was exposed to a high dosage of gamma radiation.
Mutants, on the other hand, are born mutants. Parents fear that their kids will be born "different". Mutants reinforce this fear. No one knows why babies are suddenly being born with these mutations and superpowers, but it is becoming more prevalent all the time. Parents who don't hate mutants themselves would still be upset if their kids were born as mutants, because they will be subjected to ridicule, discrimination, and even violence. And of course, there is a good chance that they may turn out to be the bad kind of mutant - more Magneto than Xavier (although most people don't make much of a distinction between the two).
Other superheroes are unique and isolated cases. There is no possibility that the world will be overwhelmed by billions of Spider-men. There won't be a million Hulks or Thors or Iron Men or whatever. They are remarkable because they are rare, and they are rare because they only exist due to some sort of mishap or unanticipated event. People in New York might not like Spider-man very much, but they also don't worry about Spider-men taking over the world.
Mutants, on the other hand, are becoming more and more common. The trend of mutant children is, if anything, increasing. There are more mutants being born every day (or at least every month or year). Therefore, whereas other heroes might be disliked, mutants stoke the inherent fear humans have of being replaced or surpassed by something better than us.
Turning to supervillains, they usually work as individuals or small groups. The only thing that makes them occasionally team up is a specific shared objective, which is generally quite temporary in nature. Once they beat their opponents or get what they came for, they go their separate ways. Furthermore, when the bad guys show up, it is pretty easy to tell who is bad and who is good - the good guys are the ones trying to stop the bad guys, and they have little or nothing in common aside from their superpowers.
Mutants, on the other hand, are split into two groups, good guys and bad guys, but to outside observers, they're all just mutants. For whatever reason, people have trouble seeing any difference between the two sides. A big part of this dynamic is probably the influence of the media: as I understand it, the press generally says "some mutants destroyed half the city" or whatever, not "the evil mutants aligned with Magneto were thwarted by the X Men in their attempt to take over the city". Chances are that if the fight was between Thor and Loki, the press would say "Loki tried to take over the city, but Thor stopped him".
All of these factors combined give us the situation you described: people hate and fear mutants far more than they do other superheroes.