I've definitely heard of misogynists, and of misogynists disguising themselves as legitimate men's advocates, but I'd never heard of "men's rights activists" as a specific group of misogynists before this.
Without this explanation, had someone said "men's rights activists are misogynists," I would have thought they were a misandrist, because it sounds like a general descriptor and not a specific group.
So what do you call it when someone who's not a misogynist advocates for equal treatment in the areas where men get the short end of the stick?