That's not the case at all. His blog is his personal blog, not 37Signals, and he has never said employees were not allowed to share political opinions outside of work.
DHH advocates "no politics at work" because as a powerful guy that's organized politics potentially directed at him. He advocates blogging because he knows perfectly well that he has a large audience and his employees or critics don't. That's why the rich tech bro class loves getting politics out of the workplace and getting it onto the platforms they own.