The last time someone tried to build a "Chinese branch of Christianity", it resulted in the Taiping rebellion [1] trying to turn China into a theocracy and millions died.

The Communist party definitely doesn't want any parallel hierarchies outside their own ranks. Where religious imagery could benefit them, it has already been incorporated into party worship/Chinese nationalism. Propping up minority religions would not be an efficient way to exert control they already have.

[1] https://en.wikipedia.org/wiki/Taiping_Rebellion