the specification of race is just like when we classify a species.
Most critters in a group share a Genus but they are subclassified in species based on physical and genetic differences.
Humans are more different.
We all come from the genus and species Homo Sapiens but there is a subclassification of differences. All people come from one of 4 basic subtypes of homo sapiens: Caucasoid, Negroid, Mongoloid and native americans (I forgot the actual scientific terms for the last one). Basically, we all derive from an ancestor that had either white, black, yellow or red skin and attributes linked to that subspecies.
These subtypes can be distinguished post mortem (when dead) via bone structure and genetic analysis.
That said, it is not incorrect to classify people by race because we are different enough that science already does so.
However, while species or subspecies may be different in a scientific classification scheme, because they share the same Genus, they can interbreed and thus create their own subspecies.
Similarly, humans do the same. Mixed race children often have a stronger combination of traits much like how a mixed breed dog is often genetically and physically stronger than the pure bred parents (pure breeding is actually bad in terms of genetic strength, check any science text on that one if you disagree).
So yes, we are different enough to be classified as race, but science aside, it is our ability to enjoy the properties of other races and interbreed that makes our offspring superior to the parents. However as humans, we can also be prejudicial and stick to races we like (ultimately to our detriment, strictly from a genetic pool strength perspective, so don't shoot me down with this one).
Ultimately, it is a waist of time to be prejudicial or to focus on labelling people bigots because this philosophical approach ultimately is not the best biological survival scheme for future children. Under Darwinian theory, those humans who are open to interbreeding among races stand the best chance of their progeny becoming stronger than the parents and this will insure that the parents genes will be continued to be passed on for years to come.
For those disbelievers, check the medical records. Humans are continually developing higher and higher incidence rates of what science classifies as weaker genes (eg. wearing glasses, diabetes, allergies, cancer and whole hosts of other genetic disorders or weaker attributes). This is the result of thousands of years of not interbreeding due to race and religious segregation.
My earlier point still stands. People are free to choose whoever they mate with (good or bad) and there are still tons of other mates of all kinds of races out there to choose from.
If someone turns you down, get over it and go to the next one!