I can understand why the Western media calls something that has an official name of CPC (the Communist Party of China) as CCP (Chinese Communist Party? Not sure here). What puzzles me is - why ordinary people always repeat this wrong abbreviation. Is it like “I never check the sources, I trust everything that Western media publishes”?

More of a "Everyone knows what CCP references and I'd have to include a distracting explanation if I want to use the more technically correct acronym"

https://en.wikipedia.org/wiki/Chinese_Communist_Party

I've never heard it called anything other than the CCP.

For something I say maybe a few times a year it’d be a great look to sneeringly point out and talk down to people every time I mention China in the context of international politics.

Unless the Communist Party of the US (I’m not looking up its official name, because it doesn’t matter) wins the next presidential election it’s unlikely that people will call it anything but the CCP. Everyone know what everyone else means.

Up until a few years ago the PRC used CCP themselves all the time. It's a handy little shibboleth. If someone calls it CPC they're probably a bot.

CCP is a direct transliteration of the characters, so that's what it started as. Some time later China decided to change it but that's a lot of cultural inertia to move in a different direction.

It was an intentional propaganda strategy to separate references to the government of an official enemy country from references to that country (see also "the Houthis" and "the Taliban"), and it also looks like "СССР."

The reason why ordinary people parrot it is because that's what it was designed for. The proper term for "CCP" is "China." Referring to the Chinese government as the "CCP" (or the CPC) is like referring to the US government as the "Demoplicans" (or the Democrats and Republicans.)

Instead, we just say "the US government" or "the US administration."