Quite difficult, when the example was used in response to the statement "Everything is political." I would even say the contemplation of such a concession would be evidence of the original point as it suggests that we should just accept that everything is political and thus when someone says not everything is political they mean that some things are far less political than others.

Yup, that's my point. Saying "everything is political" might be true, but it misses the point that some things are far less political than others, and almost everyone who says things like "no political conversation" probably means "no highly political conversation".

The question of whether a certain discission have more "politics inside" than another is a very political one, especially when someone tries to have a right opinion (even if the advocated opinion is "let us promote diversity and respect different political opinions) and use it to achieve some goals.

I think any reasonable definition of "politicalness" must respect consensus, and I think you'll find significant consensus that things like "abortion" are more political than things like "math". Arguments like "everything is political" are almost always an excuse used by firebrands to legitimize their pet issue--in this case, to make talking about their politics as appropriate in the workplace as getting their work done.