Basically, his claim is that the conservative brain is more fearful and more desirous of predictable stability, as this Alternet story describes.
Of course, there's just a few problems with that.
One is that even good science journalists can't keep up well with the spate of science announcements, some newsy, some PRsy.
The second is that arguably, per his own terminology, Mooney is a science communicator, not a science journalist.
The third is that he basically ignores both epigenetics and straight-up non-epigenetic environmental issues.
The fourth is that, on the environmental side, Chris' description could fit other things.
If conservativism is defined in part per the top paragraph, that's an almost stereotypical description of PTSD. Or even generalized anxiety disorder.
It's also just another example of a Sam Harris-type tendency to become overly dependent on neuroscience to make sociological pronouncements when neuroscience is still in the Bronze Age.
The fact is that "conservativism" is also more varied than Mooney notes, especially outside the U.S., which undercuts further any biologically reductionist claims.
And, per Mooney's talk about motivated reasoning, from previous books, he's at risk of becoming a more stereotypable liberal "science communicator."