"but also it's offensive to only refer to a person by their ethnicity/religion/ancestry, especially if they are the only charcter with that background in your story, and everyone else (from the dominant culture) isn't referred to by their background ."

For christ's sake, I am a white Church of England (perish the thought) Englishman - that is what the hell I am. You are a half China-woman - who cares?????