Honestly, this seems boring as hell.
I've often discussed politics, religion, and all sorts of things with coworkers, and we've often disagreed. And then we went about our day working together, or having a beer after work. No problems. It's just part of normal regular socializing, and I'd argue that socializing with co-workers is somewhat important for a healthy workplace.
Excessively pushing politics is a different thing of course, but "absolutely no politics allowed" has just a kind of boring superficiality to it. And also leaves us with the rather tricky question on what "politics" is, exactly.