I really think the problem is they don't understand who "people like them" actually are.
White men are not in danger of becoming irrelevant. Comics about white men are not in danger of disappearing. If you assume the comics market is a zero-sum game (and all publishing markets are, to a certain extent, although there's a fair amount of elasticity there), they may someday see a lower percentage of comics focusing on white men; but the well-written stories will survive, and survive easily.
What is becoming irrelevant is this notion that white men are the one and only important characters to write about, the only ones entitled to have adventures or to be heroes or to survive against all odds.
It's not white men who are becoming irrelevant. It's white men who want the rest of the world to also be white men, and possibly white women who are entirely subservient to them.
Oh, the host of imaginary things you'd have to be terrified of to feel like that. Poor snowflakes.
I think they also dislike that the comics that are still centered on white male characters have given the nod to people who aren't, as support characters at least. It's not so much that white, male characters are disappearing, but that ones who think like these guys are disappearing or that characters with bigoted attitudes are being challenged more in the narratives.
I am guessing that the acknowledgment that people who aren't heterosexual, cisgendered, males of European heritage exist as something other than villains or something to mock (or objectify, in the case of women) is deeply offensive to these guys. Their favorite toy is being taken away. I think the leadership of these movements are deeply racist, sexist and cis and heteronormative (or blatantly homophobic and transphobic) people. They're angry that their white, straight boys' club has been invaded by "inferior" beings.
They're whipping up followers who aren't as virulent, perhaps, as they are, by convincing them that their favorite heroes and media are in danger of extinction or that their favorite scapegoat,
political correctness, is leading industry magnates to hire inferior talent at the expense of the deserving. It's vital to them to believe (or to convince others) that the status quo--domination of our culture by white, straight, cisgendered males--reflects a meritocracy.