Republicans do not care about the truth
Republican politicians and their dysconservative supporters don't think about truth the way most people do; they are essentially counterfactualists, defending an accreted residue of wrong beliefs. Here's how that works.
When trying to decide something, a reasonable person will look at all the evidence they can find, reach conclusions based on that evidence, and then base their beliefs and decisions on those conclusions.
Dysconservatives, on the other hand, tend to treat group loyalty as more important than getting the facts right. Beliefs are not derived from evidence, but received from a trusted in-group (in this case, generally referred to as "conservatives"). They see disagreeing with the in-group's beliefs as a form of disloyalty or even betrayal. Beliefs are to be defended against any contradictory evidence, and are to be spread to others as much as possible. Every debate is a sports competition and an opportunity to proselytize; evidence is only useful if it can be cherry-picked to defend the "right" beliefs.
Since dysconservatives can never change their minds in the face of new evidence (since this would be disloyal), they end up being completely wrong about a lot of things -- and vigorously defending and promoting those wrong beliefs in the face of all reason and evidence, a practice we call "counterfactualism".
Words like "think" and "skeptical" have entirely different meanings to a counterfactualist. You're "thinking" or "using your head" when you defend or advocate the in-group's beliefs, and you're being "skeptical" whenever you question beliefs that contradict what the in-group believes, especially if you do it in a way that sounds intelligent on the surface.
While Democratic politicians are still known to have a respect for evidence and what it seems to indicate about the world, the Republican party has apparently embraced the idea that popular belief exists to be manipulated for the ends of those in power (perception-based thinking, rooted in Straussianism) and that the actual truth is irrelevant, except insofar as it can be manipulated to convince people to hold "right" beliefs.