In the events of House of M
Wanda Maximoff decimates the mutant populace, robbing them of their powers.
Does anything similar happen to non-mutants too? What about mutates?
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No one who was not a mutant or derived their powers from mutation as Wanda perceived mutation was affected. Mutates whose powers came into being via external circumstances were unaffected by Wanda's reality reset. (Beings such as Daredevil, Spiderman or the Hulk were unaffected.)
Wanda's power manipulated the existence of the X-gene, removing it from many mutants, or removing their ability to access the power. Some mutants have been restored, but the effect that allows restoration has not been clearly defined. The only thing established is it would take a significant power source like a Celestial or the Phoenix force to restore the power for most mutants.
See Why aren't more mutants having their powers restored? for further amplification.