Yes, in the comics' setting, Mutants had always existed. But before genetic science became a thing and modern science was advanced enough, people tended to see powerful individuals who lost control as possessed by demons or punished by God. In short, the explanations leaned more toward religion.
Then, during the era when Professor X and Magneto rose to prominence, human science made tremendous progress. Many scientists began studying the frequent incidents of people losing control all over the world, and they really did find what those people had in common: the X-gene.
That set everything off. People had thought this was God's punishment for humanity, only to be told that these people were not human at all, but monsters hiding among them. Back when they could not hit God, they did not blame God. Now that they finally had someone they could hit, why would they not go after them like mad?
Racism was already rampant in that era. Magneto had just begun making a name for himself among terrorists, while Professor X's terrifying ability had only just been exposed. The public's anger was ignited to its peak. Then, during an accident, it exploded completely.
The day after the New York Police Department's phones had been flooded with calls, a horrific massacre took place at a kindergarten. An extreme anti-Mutant activist believed the kindergarten had taken in two Mutants, so he grabbed a gun and stormed inside, opening fire. More than a dozen children died on the spot, while dozens of students and teachers were injured.
Then, during the subsequent autopsies, they discovered that one of the dead children really was a Mutant. Public opinion immediately shifted. People stopped blaming the killer for doing something so cruel and began blaming the child's parents instead. Why had they sent a little