It's not about "politics" as in the narrow sphere of political affairs (democrats, republicans, voting etc).

It's about "political" in the wider sense (that is "trying to be tactful", not to annoy various sides, etc).

No, that's a false etymology. The term "politically correct" in its modern usage came from leftist movements in the 70s to describe politics (not in the broad sense of "tact"). Think of it as a synonym for "ideologically sound". The civil rights movement was definitely about politics, not tact. The term "politically correct" was then appropriated by the same leftist movements and used sarcastically to parody themselves.

Afterwards, it entered the general lexicon.

It's not about etymology. It's about usage. The term has a long history and differing uses. The etymology does not matter (it rarely does, and if it does it's mostly for historical reasons).

It's the use of the word that matters.