I've been following MT for many years and the politics at work cast, whilst interesting, was one of the few that didn't cross the Atlantic too well!
My view is that in the UK a level of political discourse is almost expected, especially at a senior level. The gold rule is to be measured in your comments and certainly not to appear extreme in any way.
Similarly my firm (a multinational), like many others, encourages participation in the political process.
Now religion at work... that's a whole different kettle of fish!
Contrast my brother-in-law's US firm where participation in morning prayers is expected. I don't think that would ever be tolerated in a UK business.