^Or if it's a slightly alternate universe where anti-mutant hysteria isn't so widespread. (Although the crossovers went both ways; there was a late X-Men
episode wherein a news van had the J3 Communications logo from Spider-Man
Then again, maybe it's just that Spidey mostly operates in New York City proper, which is a very cosmopolitan city and might be more tolerant of mutants, whereas X-Men episodes were often set in other parts of the world. Although they did do a lot that was apparently set in Manhattan or thereabouts, so that doesn't entirely work.
As for Wolverine&tXM/Avengers:EMH
, there's apparently some time that passes between them, so maybe there were intervening events that eased anti-mutant tensions; maybe the X-Men preventing the rise of Apocalypse (as seen in the cliffhanger ending of the first and only season) led to improved public opinion of mutants. Although I'm led to wonder where the rest of the X-Men were in the later EMH episodes that Wolverine appeared in. It seems odd that none of them participated in the series finale when just about every other major hero was involved.