In regards to Godot, the account manager should not have picked a fight with a random person on social media (even if they find them annoying). By calling themselves "woke", it taps into a pre-existing idea that woke means someone who is politically correct, a stiff, and pedantic (this is how the term is seen among a number of people).
What they should have done was ignored someone's random take and said something like "hey, who has built a game with characters who are LGBT?". I don't think anyone would have batted an eye, if they did that. The way they handled the debacle was also quite unprofessional and only poured fuel on the flames.
Was that response to them warranted? Maybe not, social media isn't a nice place. That said, the account manager should have avoided getting involved in social media drama to begin with.
And yes, it does get pretty silly. Social media is like that (particularly that site).
It's a bit tricky because it's probably not that easy to tell what is going to take off (in a bad way) and what isn't. We have the benefit of hindsight but maybe they didn't.