Why can't they? Anyone should be able to have the religion they choose (including none). Restricting one group of people from any religion because of race is wrong. So, then, the question is "why not?"
Unless there is something that I don't know about. I don't keep up with news that much.
Yes of course they (you) can. I have Chinese christians that attend to our church regularly. So you can stop worrying about it. In the bible it says God has grace and compassion and love for every one. The Bible dose not lie. The Bible dosen't say God has grace and compassion and love for everyone except the Chinese! God isn't racist!
I'm half Japanese, but I still believe in God. I'm a catholic. Of course, in china, the government has outlawed the Roman Catholic Church. They have "The Patriotic Catholic Chinese Church" or something. Instead of swearing allegiance to the pope, the priests and bishops swear allegiance to the dictator or emperor or whatever.