In my opinion race is about one's genetic characteristics rather than religion or country of birth.
North Asian, Eskimo, American Indian, Australian Aboriginal, Caucasian, African, Persian are all races.
Here's the quote from the Oxford; Race refers to a person's physical characteristics, such as bone structure and skin, hair, or eye color. ... An example of race is brown, white, or black skin (all from various parts of the world), while an example of ethnicity is German or Spanish ancestry (regardless of race) or Han Chinese.