Anyone being unbiased who claim to know enough about PRC to point at the state being behind it doesn't use the wrong and derogatory term for the Communist Party of China ("CCP", it's CPC). That's like 60 minutes making a documentary about the Federal Investigation Bureau or the Party Republican.
That's like claiming it would be derogatory to label the URSS as USSR or the KPD the German Communist Party.
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.
I skimmed that page, and all I found was some group stating that placing the country name before the party name is somewhat racist. Which I suppose could be an artifact from when Lenin and Stalin were trying to incite world revolution through the Comintern, when the communist movement wanted to eradicate all borders and make the whole world communist.
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://www.jordanharbinger.com/sam-cooper-how-the-west-was-...