He was trying to do the whole "supernatural stuff is actually science fiction" angle. In this case, he was trying to go for the idea that Angels, Demons and other divine and diabolical beings from the various Abrahamic religions weren't actually divine beings, they were ancient mutants who formed factions and started to war among themselves. Not a terrible idea, but one that proves difficult to do when you consider the X-Men are still supposed to be part of the Marvel Universe which has actual demons in it like Mephisto, Satannish and D'Spayre (unless they're secretly ancient mutants too). Jack Kirby's Eternals kind of had a similar problem with its characters having supposed to be the sources for the various ancient gods. It doesn't work if Thor is right there.
But yes, rest assured, Azazel is a mutant.