Even allowing that it is gendered (although I’ve seen enough “male Karen” vids and articles that that’s not so clear-cut anymore), that’s not the same as misogynist. For comparison - “Chad” used to refer to some dude-bro to isn’t misandrist, even though it’s as gendered as Karen if not more so (never seen a Buzfeed list of female Chads, for instance. I have of male Karens).
And no, I don’t accept this kind of bullshit from privileged men any more than I do from privileged women.