What tends to prompt such responses in my experience is saying anything along the lines of "In my experience, I've noticed there is a tendency for (insert gender) to..."
Actually, in hindsight, the inflammatory responses mostly only happen when the inserted gender is women.
In these situations my default is to just observe as dispassionately as possible. If I'm in a cheeky mood maybe I'll troll a bit or try to find a humorous way to point out how the shoe could be on the other foot. And sometimes, although very rarely, the mood is just right that I feel safe enough to be earnest.
If I got all up in arms every time someone says something misogynistic or misandrist, I think I would end up being a very lonely person. I've seen a lot of these people. They either end up brainwashed on one end of the gender war spectrum (and usually just so angry and spiteful -- this is the polarized archetype), or get cast out of all possible ingroups if they make the mistake of attempting to be too consistent with their criticism (nerdy and socially unaware archetype).
99% of the time something is described as woman-hating, which is what that word means, it's nothing of the sort. But feminist extremists react so extraordinarily over the top, and our culture unfortunately forbids firing people for this type of OTT reaction, that everyone else lives in fear of triggering them.
So help everyone out here. Next time you think you've heard something "blatantly misogynist", stay out of it. Let people talk.