Of course it is exaggerated. That is the point of a hyperbolic arguments.
Examining hypothetical edge cases in more detail is a useful tool for defining where the issues lie in a debate.
Would you support/play a game of 100+ devs if key management DID commit war crimes? I'd like to think probably not.
It's though it is clear from your response that misogyny isn't a deal-breaker for you for this case, so the question then becomes; how shitty does a single person need to be before it becomes an issue for you then?
Other people drew a line in the sand at misogyny and there is nothing wrong with that. In fact I'd say it is a respectable opinion.
You probably would prefer to just ignore any controversy and just judge the game on its merits alone, and that is fine in its own way too. It is exhausting keeping up with the news and you would be happier and find it easier to just blindly enjoy a game.
But don't pretend that just because you are ignoring it, doesn't mean that you aren't supporting bad practices like misogyny when you do so.
Talking about it would be enough.
It would find it's way to a citizen that could make a difference.
There is a reason most modern dictatorships restrict access to the the Internet.