A recent discussion with a right-winger has given me a possible insight to WTF is going on with them, but there's still some work to do towards laying out the evidence.
While it's still fresh-ish in my head, though:
We all understand that there are limits to what we can reasonably call "facts", because there's so much we don't know about the universe -- but people have an emotional need to cope with the non-factual parts of life, so they fill in the gaps with stories that help them feel safer and more in control.
Historically, people organized around these stories: if a lot of people believe the same thing, then it must be true, right? So being together with other people who have agreed that a certain set of stories is how things actually are is comforting, because it gives them reassurance that they're not just guessing.
Those groups of people become "religion", and the stories they believe become "doctrine".
(I think this must be the origin-story for "separate magesteria", which posits that some beliefs are testable, but others are not and never will be, and therefore can only legitimately be settled by doctrine rather than science -- even as the science shows otherwise.)
The problem with this system is that right-wing authoritarian followers seem to be all too willing to include whatever they don't understand as part of the doctrinal realm -- and once they have accepted something as part of that realm, it becomes an integral part of their emotional safety-net, i.e. the set of stories they need in order to deal with the unknown.
Right-wing powermongers -- maybe think of them as "faith-emperors" -- have learned to exploit this tendency. They see ignorance, uncertainty, and confusion as unconquered territory they can claim (in the name of whatever faith will have them) by creating new stories around it.
Those stories are, of necessity, completely counterfactual. Stories that correspond to the evidence are part of science, and accepting those stories would be ceding territory to an enemy power.
This is why they get upset when we try to show that their beliefs about reality are in fact testable, and that the evidence contradicts their doctrine.
When we say "what you are doing is harmful", they see us trying to destroy their faith because we're attacking their safety.
They see us as trying to invade territory that rightfully belongs to them.
...or something along those lines, anyway.
