Well, a Jew who's studied Torah would explain it better than me. But according to Hallacha, Christianity is Shituf ( that is believing someone or something helps Hashem to guide the world, it may be Jesus, a star, etc....). Shituf is Avodah Zarah only if done by a Jew, but not by a goy. Worshipping some idol or power and believing it is independent fron Hashem is Avodah Zarah for both Jews and Gentiles.
There are several reason not to have or buy anything made or used by an idolator.
1- The idolator may have devoted the object or his effort to an idol.
2- If you have trade, sell or buy from an idolator, he may use what you sell to him or the money you pay to commit idolatry.
Atheism is also forbidden for both Jews and Gentiles, but there is no problem with having trade with them. Thier objects are not devoted to any idol, and he won't use the money to commit atheism. For example you may sell a candle to an atheist since he would use it only to light his house. He is a sinner, but you don't help him to sin even more.
I'm not an expert about far East culture, but I think most Chinese are Budhist or Confucianist, those are philosophies, not religions. Budhism is a form of Atheism, and it would be forbidden for goyim also, but you are not forbidden to have trade with them.
Anyway, nowadays it is nearly impossible to follow those rules. Even a Christian by name, may practise Avodah zara superstitions. And I would dare to say that there may be also Jews who commit idolatry.
If you really want to know what to do, then you'd need a Rav.