It's a shibboleth, there are people who use CCP who are not anti-China but people who use CPC are more likely to not be anti-China. I wouldn't get caught up in the name out loud with someone.
Historically both names have been used when localized into English. Though there is an argument to be had the CCP implies some sort of international communist cabal (a la red scare) while the CPC is more accurate as the Communist party is just one of the many political parties in China (including autonomous govts in Hong Kong and Taiwan).