Actual study for the lazy. I think we need to be careful about the whole US centric nature of it. For one, the lines are usually a lot sharper. For two, i'm sure the culture and enviroment you live in as a whole does have a massive effect on your psychology, so, this would only be true for a specific place (the USA) and a specific time (the 21st century). I think it would be interesting to see if they could replicate it across other cultures.
Our political centre of gravity is in a different place compared to the USA. Roughly 50% of Aussies support our "right wing"/"conservative party" but it doesn't have the same nature as the counterpart party, the republicans, in the USA, even though the numbers and split is roughly the same.
I think it's also important to note the direction they're saying it's caused in. It's not so much people with a specific brain structure will vote for X, rather that believing or thinking Y will change your brain. This isn't really new. Drawing on things like depression research, many people know a malfunction in the brain in one way or another will cause people to become depressed, i don't want to use the word "chemical imbalance" because that theory is horribly outdated but like that. So, basically, changes in your brain will make you sad. We're seeing a bit of evidence now that it can also work the other way, if you're under a lot of prolonged stress or socially isolated or other situations like that, these emotions can feedback and change your brain.
It actually relates to an issue in philosophy called "peer disagreement" as well. If you have two people who are intellectual and cognitive equals, why do people make different choices? My focus is on religion, so, there is an example for instance. There are many people who are just as smart, intelligent and considered than us and they made a different choice, why? So, i guess conceivably, we could put down at least a little of that disagreement to neural aspects like this.