A few basic facts to bear in mind: Most genes influence more than one trait. Most traits are influenced by more than one gene. The development of a complex organism like a human, especially brain structure, is massively influenced by the environment, which interacts with the genome in highly complex ways as the organism develops. As a human learns and develops and changes his ways of thinking, the brain physically re-wires itself to reflect those changes (in fact, the brain re-wiring probably is those changes).
The idea that genes could determine political views in any simple or straightforward way (never mind "political views 'hard-wired' into your brain", in the words of the article's amazingly-stupid headline) is immediately belied by the fact that very many people change their political views over time; in fact, some people change their political views drastically and quickly as a result of a single experience or exposure to new ideas. For that matter, the very meaning of political right and left varies over time and from place to place. In the US, the left-vs-right divide is primarily a matter of secular vs intensely-religious world-views, and church attendance correlates with voting patterns better than any other factor does; in Britain, where this story originates, both left and right are mostly secular and the differences lie in other areas.
Looking at the specifics of the story:
It's quite possible that there are genetic propensities to be fearful and irrational, and that some people's genomes contain genes which code more strongly for that trait.
It's quite possible that people born with genes which predispose them to be fearful or irrational are, in fact, somewhat more likely to grow up to actually be more fearful and irrational than average, although I'd expect that any such predisposition would be mostly swamped by the influence of life experiences.
It's quite possible that people who are more fearful or irrational than average (whether the main reasons are environmental or genetic) have brain structure which visibly reflects this.
It's even possible that people who are more fearful or irrational than average (whether the main reasons are environmental or genetic) are somewhat more likely to become more politically conservative, although one could easily think of a dozen other factors which would likely have a larger influence on a person's political views.
So, yes, there could be some correlation between genes and political views, but it would be too fuzzy and indirect to tell us anything of value about actual people.
Look, it's only a few decades since some people were claiming that blacks or women were genetically hard-wired for traits that made them unsuited for full citizenship. Enough is enough.
About the whole idea that something as complex as a person's world-view could be genetically determined in a straightforward way, I liked this item -- but at least it was intended as a joke.