There is nothing inherently Republican about disliking science, nor can the supposed neurological traits of the conservative—rigidity, fear, aggression—be correlated to efforts to ignore or suppress scientific findings. (Mooney uses conservative as a synonym for Republican, though this is not strictly speaking true.) At best, conservatism can be correlated with specific reasons for suppressing or ignoring certain types of science, especially politically-inconvenient science such as global warming and evolution. Conservatives continue to support applied science, including technology, oil exploration, and nuclear power in large numbers.
Conversely, liberals, whom Mooney identifies as open-minded, tolerant, and enamored of ambiguity, are no firm supporters of science either. Liberals have embraced such pseudoscience as homeopathy, astrology, ancient astronauts, and anything New Age. Liberals, according to surveys, may trust science more than conservatives, but this depends on what we define as science. Liberals are more likely to think that non-science is actually science or an “alternative way of knowing.” They’re still advocating for beliefs that aren’t true at the expense of science. They just don't think that's what they're doing.
This is why I dislike partisan claims that one ideology or another is to blame for America’s retreat from science and reason. Had this book been written 40 years ago, it would have been called The Democratic Brain and complained about how liberals were pushing anti-scientific social welfare policies and advocating for alternative medicine. Mooney has previously written about alternative medicine, so he is not unaware of this problem, but overall the thrust of his writing matches the thrust of his politics.
The fact is that despite the euphemistic term “political science,” politics is not a profession governed by reason, and self-identification with a party or ideology virtually guarantees embracing some anti-scientific ideas since ideologies of any stripe are defined by adherence to dogma, the very opposite of science. The short version is this: People support what they like and oppose what they dislike.