One candidate could be brain systems controlling our emotional responses. For instance, a study showed that American volunteers who started to sweat most when they heard a sudden noise were also more likely to support capital punishment and the Iraq War. This implies that people whose basic emotional responses to threats are more pronounced end up developing a constellation of more right-wing political opinions. Another study, this time in Britain, showed differences in brain structure between liberals and conservatives – with the amygdala, a part of the brain that learns emotional responses, being larger in conservatives. Again, this suggests that differences in political beliefs might arise from differences in emotional processes.
But notice that there isn’t any suggestion that the political opinions are directly controlled by biology. Rather, the political opinions are believed to develop differently in people with different basic biology. Something like the size of a particular brain area is influenced by our genes, but the pathway from our DNA to an apparently simple variation in a brain region is one with many twists, turns and opportunities for other genes and accidents of history to intervene on.
So the idea that genes can have some influence on political views shouldn't be shocking – it would be weird if there wasn't some form of genetic influence. But rather than being the end of the story, it just deepens the mystery of how our biology and our ideas interact.