Race is compromised of many factors. I'm not sure if by appearance you simply mean skin color. There are people of varying skin tones throughout the world who do not necessarily belong to identical classifications even though they share similar pigment ranges.
Very simple examples are the invalid use of Caucasian when the stereotypical members of the grouping can range into the color spectrum traditionally thought of when viewing Arabic and Indian. In fact quite a few individuals that fall genetically as Arabic and Indian can range light enough to be considered traditional Caucasian skin tones.
I think it's more important for people to identify with the cultural ques they respond to rather then the skin tone they subscribe to as that can give the outside observer a better foundation to make a judgement of their personality. White people do not always wear monocles and talk down to people, but more often then not if you meet a person in a tuxedo, monocle and cane he probably wants you to think he has money.