I seriously doubt it. I don't know of anything interesting that has come from discussing non work-related politics at work. What needs to be preserved is the ability to discuss work-related politics at work, which can currently easily get you fired (but for a made-up reason.)
As for companies not talking about politics, I don't care what companies have to say. They're the mouthpieces of their owners. As can be seen in this case, when the owner dictates that the company doesn't participate in politics unrelated to its business. Should companies have the right to speak about arbitrary subjects, but not the right to silence? How can an employee feel like they'll be treated fairly if they don't agree with the company line (issued yesterday) about apricots in Africa?
I'd go farther and say that the list of subjects that a company opines in public about is the same as the list of subjects an employee can feel like they're not free to have an opinion on that anyone at their job could hear about without risking their livelihood.
The fact that DHH goes on and on about politics in his personal life but keeps it away from the company is a positive indicator that it's not opinions that are being suppressed, but opinions about business-unrelated political matters on internal systems.
edit: I feel that a priority for any sort of socialism, or civilization for that matter, is to figure out how to work productively with people you don't like or agree with. And psychologically, not being able to cooperate with people who differ from you is an issue of autonomy and boundaries.