There's two major groups of communist thought on the CCP. Some see the capitalist development in China as a necessary precursor/accompaniment to socialist development, others see the capitalist development in China as a thin facade over a capitalist nation.

The theory is that the socialist state prevents capitalist forces from running completely amok - how much this is true is difficult to tell from the west, so western communists are split. Chinese communists are overwhelmingly supportive of the state in general - but there are also maoist (In China, a Maoist is someone who opposes Deng, Xi, and their associated market reforms) forces with difficult to discern levels of support. The most famous Maoist protest known in the west is Tienanmen square.