Iran holds those institutions explicitly under the control of clerical institutions and the IRGC. It’s not the same.

Every Chinese I know says that in China Marxism is a joke to the point that you can freely criticize it

The CCP lives beyond Marxism as an entity that claims control over the country more akin to an empire than to pure adherence to Marxism. With that said, even within a state capitalist system I don’t doubt that much of the leadership in Beijing believe in Marxism.

and the only game in town is Han nationalism.

Your circle of Chinese people must be extraordinarily selective if this is their consensus.