Then again, I don't care if someone thinks that a reference to a communist party is negative, as long as the negativity is about the communism aspect (as opposed to the ethnicity or general culture of that country). Just like I don't care if the NSDAP would find it insulting if I call their party the Nazi party.
Also in your link is a reference to the official CCP website, where they themselves (or so the talk page claims) state while they prefer CPC, CCP is also acceptable.
So it seems to me that this is a nothing-burger, where some activists are fighting on behalf of a group that doesn't really see the reference as a slur in the first place.
Based on this link, CCP was even the original abbreviation, which was changed to CPC as late as 1943 due to pressure from Comintern/Stalin:
https://chinamediaproject.org/2023/03/30/ccp-or-cpc-a-china-...