The idea that you can't judge someone's race by their genetic inheritance alone seems to be an almost absolute truth based on much of the research of the Human Genome Project (HGP) and the information contained on sites like Ancestry.com. In short, genetic research has established that we are much more alike, genetically, than most people ever imagined.
That concept seems academic, perhaps a bit much for the average person who will probably never read the scientific journals or the reports of the HGP, but Ancestry.com and other sites like it have democratized this research and made it easily understandable to almost everyone.
Ancestry.com reports (and I have first-hand knowledge of their content) break the complex genetic code, made up entirely of an almost infinite combination of A, C, G, T (the chemicals which make up DNA), into very simplistic terms anyone can understand, reducing the information into percentages. Mine, for example, indicates that my ancestry is roughly 25% Italian, 25% Portuguese, 40% Anglo-Saxon (English, Irish, German, Nordic) and 10% a mixture of many other ethnicities, including African.
In certain academic experiments, students are asked preliminarily which other students in the class they are most closely related to genetically. Based on common sense, most of the caucasian students choose other caucasians, Asian students choose other Asians, and African-Americans choose those who look the most like them. When they receive their ancestry reports, many are shocked to learn, for example, that some caucasian students are much more closely related, genetically, to African peoples than to other caucasians. This generally holds true across ethnicities.
The HGP has thus obliterated the idea that because we look alike, we are more alike genetically. In the context of this discussion, that means that, if we are all much more closely related than we thought, it is ludicrous to suggest that one can judge a person based on physical characteristics. Our "genetic inheritance" as it relates to race and ethnicity, means almost nothing with respect to individual characteristics. "Race" is simply a combination of molecules, many of which are possessed by the entire human population. "Race," on a molecular level, means nothing; it is entirely a social construct.
Genetic race and ethnicity, as established by 23 and Me reports, for example, do not reflect anything about someone's culture. Your genome says nothing about the art your personal culture produces or its music, political structure, child-rearing strategies, technology, or any of an infinite number of ways in which cultures differ.
Genetics simply cannot account for anything other than who we are physically (eye color, skin color, height, etc). Races and ethnicities must be judged on an individual basis, person by person and society by society. This has proven to be true scientifically, socially, culturally, technologically, and ethically. We are far more alike than we are different.
An interesting side-note—the anthropologist Jared Diamond, in his book Guns, Germs, and Steel, posits that the relative characteristics of races and cultures is also hugely influenced by geography. Harsh climates produce different levels of societal development than mild climates do, for example.