State-lead religion has long been known to be problematic, particularly in the west, and more particularly in the United States. Today the United States has separation of church and state. This principal is properly understood as a reaction against the Anglican Church, wherein the government had both religious and political power. Before the Anglican Church was the Holy Roman Empire, and other such cases exist further back in history in both Rome and in the Middle East.
In the past, China’s secular government has had a policy of banning and censoring Christianity. That may be changing, or it may be continuing with an additional layer of opposition. Rumor has it that China will be providing a translation of the Bible with its own commentary.
An official, state-backed translation and commentary of scripture will plausibly be much more effective in modifying theology to suite the preferences of government in comparison to a ban on Christianity. Keep in mind that the preferences of the Chinese government are still perfectly secular and anti-Christian. It’s not as though the Chinese government has converted to Christianity.
This is very similar to the approach I have recommended to stamp out Islam, by the way. Physical war actually preserves the real problem in Islam, which is the information rather than physical violence. The latter is an outcome not a source. Only by addressing the information head-on will the outcomes be addressed in an effective, sustainable way.
Key difference? When the Chinese government manipulate Christianity, the people lose a truth and gain a lie. When Christians and Muslims engage intellectually, rather than physically, lies tend to be lost and truth gained.
Another key difference is that many people within and without China weight the opinions of that government very heavily. It has been reported that there is an institutional trust crisis in the United States, while institutional trust in China runs high. A trust crisis would benefit the purity of orthodox Christian theology in the context of state support for biased translation and theological work.