Apples and oranges. Politics triggers people at an entirely different level, to the point that many can't let it go.
Basecamp's decisions may not make sense if you've only worked with level-headed coworkers who are capable of disagreeing with each other on politics and still maintaining respect for each other. However, once you've seen what happens to offices where people let their angry political debates from Facebook and Twitter spill over into the office, it makes a lot more sense.
Company chat shouldn't look like Twitter flamewars or Facebook rants. Some people can debate things and then check their feelings at the door when it's time to get back to work, but many can't.
I think it's fairly easy to make the argument that our minds are especially tuned to tribalism. Not only that, but what comes out of discussions focused on political/social tribalism is especially toxic. It's one thing to have a little banter about football teams, it's another when people are convinced their lives are at stake.
huh? their lives (and livelihoods) sometimes are at stake...
A place where you have to only "be about work" is impossible to achieve. Even sweatshops in Bangladesh have unions and places where they can talk politics.
I would say a healthier choice for them would've been to cut out the people that were bullshitting and causing toxic environment. For sure those exist and should be spotted if they cause negativity at work.
Funny thing is that doing this top-down, as they are doing, is literally "cancel culture".