Well, people from different genetic background are likely to be subject to different hair care needs, dermatological problems, and so forth. "Race" is a tricky word because it can have both genetic and cultural connotations. For example, Jews can arguably be classified as a race in spite of their genome having long since become so diluted as to make it a bit silly to assume that most of them will share the same genetic characteristics. In the genetic sense, race can be tied to a consistent likeness in genetically passed physical characteristics, but, in such places as America, even this can be tricky because, for example, the "black" population is, on average, about one third European according to something I read on the subject a long time ago.
Though it is a tricky word and sometimes causes too much confusion to be useful, however, the word is technically correct when used to refer to a group of people that consistently shares a particular set of genetic traits. This has become problematical mainly because it has so frequently been used to refer to a stronger division than is deserved or referred to in terms such as "black" and "white." There is no "black" race, for example. The pigment is due to a fairly weak phenotypic variable. There is more room to argue that Australian Aborigines are a seperate race from gene pools related to, for example, the Hutus than there is to seperate black and white populations that are known to have had a long history of exchanging genetic information, and there is even reason to believe that it is less proper to seperate aborigines from native Americans than to classify them as seperate from some African populations.
I think that it would be more useful, on the whole, to go with self-identification. If one has most of the traits that could give one grounds on which to identify as a member of a particular race, one may or may not self-identify as a member of this group. One might prefer to classify oneself as "mixed," which, in most cases, would be perfectly proper.
