The word "共产党" in this context just refers to the Chinese Communist Party, or which else Communist Party would the viewers think they're protesting against?

If I literally translate it to "Communist Party", it's too cumbersome, since the original word "Gong Chan Dang" has fewer syllables thus takes less time to say. Using the acronym "CCP" is a perfectly reasonable approach, since it also has few syllables and the meaning isn't that inaccurate. If I use "CP" it's just confusing.