You would be surprised how much Christianity is rooted in China. I know of at least two large active churches in Shenzhen and when I was up at Wenzhou there were half a dozen spires visible from air traffic. Most of them in Wenzhou had been taken over during the Cultural Revolution but not far down the road was a brand new church. Not a small one either, about the same size as a four storied block of flats.
There is a running spat between Beijing and the Vatican. The problem mainly revolves around people. China demands total loyalty to the State but it can accept loyalty towards gods, be they Christian, Muslim, Hindu or whatever. The problem with the Catholic Church is the Pope, and the infallibility therefore. He is a living thing, not a deity so that belief is unacceptable.
I believe that the Catholic Church in China has now reduced the importance of the Holy See to acceptable levels.