Some part of these differences is from rearing and culture, but massive variation exists even within the same household.The same household implies family implies related genes. This is just another case of overreaching evolutionary psychology. While our basic actions and social personalities are from biology, specifics like individual political beliefs are not easily linked to anything so simple. To be fair to the researchers, though, it is probably (definitely) being misrepresented.
There are genetic components to some broad personality traits. As I mentioned with lower IQ trending towards conservatism, but party affiliation and individual issues are related far more to the area and family you were raised in. In fairness, I will read the article and update if I notice any convincing arguments.