Won't People Fear Mutants More, If We Call Ourselves Mutant Hunters?

Lately, I've been on a X-Men: First Class kick and I've just been reading the 3 TPBs that have been published and while being on this Original X-Men jag. I've been wanting to read just about anything with them in it as a team. So, the other day I was reading some stuff online about the original X-Factor book and it got me thinking of the terrible idea it was to create the team as a group of mutant hunters and yeah, I know they were being manipulated by Cameron Hodge. But, still didn't any of the original 5 think that was a terrible idea? Even Beast? Granted he is a super genius scientist who's greatest accomplishment as accidentally turning himself blue. But, still... Heck, even Cyclops should have had an inkling that this was a terrible, terrible idea. granted because of my age I'm not too experienced with the early issues of X-Factor, since, by the time I started reading comics Angel had already gotten his metal wings and Havok was leading the X-Men. I just find it weird that it doesn't seem like any of the original 5 that this was the terrible idea it was until Cameron Hodge and Apocalypse had manipulated them into creating more fear of mutants in the general populous. Of course, the one thing this premise had in its favor is how in general the normal people of the Marvel Universe seem to not like or trust superheroes far more than in the DC universe.