Upon reading the New X-Men series of comics it suddenly struck me that the concept doesn't hold up as part of a wider Marvel universe.
The X-Men storylines, as an allegory for racism, is watered down by the existence of beloved superheroes inhabiting the same world. While it's true that the mutant issue has a tangential relation to genetics and a fear of the Homo Sapiens Sapiens of being replaced, i think it would only be logical for this fear to extend to a bulking mass of inraged destruction like the Hulk or even more humanoid superheroes that still display capabilities beyond natural humans like Spiderman. Specially considering that a mob guided by an "Us against them" way of thinking would hardly care to run DNA analysis for each individual that could potentially threaten their whole species in order to determine if they're mutants or simply a recipient of some miscellaneous radioactive accident. Either way it shouldn't make any difference since it has been stablished that some superpowers obtained incidentally can be passed down to the individual's descendence, namely the sons of Mr. Fantastic and Invisible Girl.
It also should be pointed out that other superheroes do go through a phase of, let's say, impopularity from time to time. However, this is most often due to specific actions of said hero or in atypical examples of widespread opposition to superheroes, it's originated for a concern over what superheroes do, not at the very concept of them (The whole Civil War storyline)