Comment by lynguist

I have come to understand that "no politics"/"just politics" means no election campaign talk.

As almost everything that is personal is in some way political (when taking the meaning "what strategy to use for ruling over a city") even the discussion of what politics is can kill discussions. (Like it seems to have happened in your example.)

So my conclusion is you cannot separate "personal" and "political" into completely disjoint categories.

The rule seems to be in place to make discussions not veer off in direction of which policies to apply/to be in favor of which particular politicians (which is nowadays the biggest taboo for a corporate LLM).