First, the executives absolutely clamped down hard on a discussion about workplace behavior. I think their attempt to cast this as “political” is deeply cynical; discussing how people behave at work will always be in bounds, even if it touches up against issues that are politicized. The initial trigger here was a discussion about the list of “funny names”; there’s no easy way to sweep that under the rug as off topic, since it’s explicitly at-work behavior.
Second, they did an end run around the employees. Announcing the policy to the world, and implying that the Basecamp workforce was having a problem focusing on their jobs was an asshole move destined to blow up in their face. Nobody likes feeling crapped on by their boss, especially not in public like that.
Honestly, it didn’t have to be about politics. Treating employees like that, especially ones with options, is typically not going to go well.