I don't think the Eternals do hate the X-Men. And I think your question should be 'why do the public hate mutants and not the Avengers?' which is a valid one and one which is why I would actually prefer the X-Men aren't part of the MCU, because it makes more sense if mutants are hated and feared when they're the only ones with powers, but not when people like Cap, Thor, Spidey et al are being lauded as heroes.
Comments
Who is Thor favourite rapper - MC Hammer
Iron Man, Cap America and Hulk build Ikea Wardrobes in Avengers Assemble
Oh this is the fresh one "fix" a 3.5 years King Pin bug.
One says, "you man the guns, I'll drive."
"You're bad at battlegrounds... and that's ok."
"Time is not a resource in the contest."
"What is this, some kind of a joke?"