Imagine that a coworker keeps misgendering you, and that commenter is your manager. Your workplace has a “no politics” rule. Who do you think will be told to stop being “political”?
I also don't think that someone politicising something makes the "other side" political automatically.
If Basecamp hired a retrograde sexist that called unmarried women "whores" in the hallway, the women would have all the right to complain, and it wouldn't be a political discussion. It would be just be (in a perfect world) HR vs Asshole.
EDIT: Also I'd like to say that I'm not condoning banning politics at work. We probably agree on most things. I'm just saying that co-workers, managers and the company being reasonable makes way more difference than politics/no politics. Unfortunately there's no perfect solution to the problem of people being unreasonable, other than those sociopaths ceasing to exist.
The retrograde sexist thing sounds obvious because public opinion there is so one-sided. But that's not true for all issues. It was legal to fire employees simply for being gay or trans less than a year ago.
I think we're mostly on the same page here. I agree that ultimately, assholes will find a way to be assholes regardless of the policies in place. But we should still be wary of policies that give them cover to do so.
What I am saying is that someone forcing an issue doesn't make "both sides" political by decree. A person being misgendered can still bring the issue with HR without it being political in a way that's against any kind of political conversation.