I think the GP comment is referring to LGBT people who are out, willingly or not, to their coworkers. Which bathroom a trans person uses, for example, is considered a political issue by some people.
But I also think that point can be generalized, to the boring but obvious conclusion that everything involving interaction between human beings is political, since those interactions occur within the context of a malleable political system. We could theoretically pass a constitutional amendment that makes being late for standup punishable by prison, couldn't we? Is it now political to be late for standup? You end up arguing over the degree to which something is political, which leads back to what everyone is complaining about: the enforcement of this policy cannot be anything but arbitrary.
Personally, I think that if the Basecamp folks want to ban a particular type of politics then they should grow a spine and say what they mean, instead of expecting everyone to read between the lines for them. If they did that then perhaps they could expect people to agree to disagree, but these guys clearly know what they want to say and the only reason they don't say it is because they know how bad it makes them look right now.