Your scenario is basically describing a guy demanding that his coworker be fired because 90% of the content on her social media channels consist of some variation of "men are trash".
I'm not talking about firing them, I'm just asking if you'd now feel uncomfortable working with them?
Even worse so, if you complain about misandrist words like “mansplaining” or “techbros” being used AT work, nothing will happen. This is purely one sided and makes workplaces extremely toxic.
you'll need to give me details about how this manager would actually treat me in this hypothetical situation
if my manager constantly tweeted content that made it seem like they hated men in tech, but treated me fairly, why should I care about what they post on twitter?