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Different parts of the MCU multi-verse. With different histories.
In any case, Mutants are more dislikeable because of the damage they cause. They are "among us".
People might accept violence of a sort (wars, foreign countries) but they don't want "weapons" going to school with their own children. Also the mutant gene could be seen as a genetic flaw in humans which affects future survival of humans. Like how yt people (as the theory goes) dislike non-white people because of genetic annihilation threat. Unlike super-heroes which carry no such threat.
In reality if there was a group of readily identifiable people with a gift that could lead to them dominating others humans would partition them off. Jews for example are seen as problematic because they "'put each other first" and are "smart" and "rich". Other people that society loves may share those qualities but don't get the hate because of the folklore surrounding them. People love Steve Jobs but hate Soros.
If mutants injure a few kids, crash a few planes, are spoken about as being better, use their money to get rich, stick together, look better, are smarter etc people would turn on them even while liking the Avengers. They'd probably see them as the bad guys and expect the Avengers to do something about the mutant problem.
