How do the comics reconcile the existence of mutants as stand-ins for socio-political minorities while apparently ignoring or "giving a pass" to other super humans?

While it's yet to really come to pass in the cinematic universe, I assume that X-Men exist in the same general universe as all the other non-Mutant super humans in the comics. Is there any in-univetwe explanation as to why they specifically appear to be the stand in for civil rights/LGBT+ controversy while the other superhumans in that shared universe do not suffer the same social stigma?