My pet theory traces it to the 1970’s:
Watergate drove away a great number of those who would have been the next generation of principled Republicans. The sort of pol, and the sort of voter, who were generally in favor of corruption, blatant lies, and abuse of power remained–and they set the new tone in the party.
Reaching out to “white, socially conservative evangelicals” was supposed to help their numbers, but that eventually meant not only appealing to, but recruiting from, some kind of wacky people. Conspiracy theorists, racists, Pat Robertson fans, and so forth.
Nixon already had influential Church-of-Christ,-Scientist types in his administration. In the wider secular culture, they became villains. In GOP-oriented circles, they became some of the martyrs of the persecution of the conservative “good guys” in Watergate. Fundamentalist churches spent twenty years handing out books by Chuck Colson and comic books by Al Hartley. Eventually, they had a religious movement of vaguely Nixonoid “holy warriors” who would stand up for an unrestrained executive and for Nixonian lawless authority against those eeevil libruls.
I’m less certain about this next part, but I suspect it’s part of the story. The worldview became flavored by “Christian Scientist” idealism, as follows:
[ol]
[li]Reality to a “Christian Scientist” is essentially subservient to Mind.[/li][li]Therefore, a non-teleological universe, as in Gouldian evolution, is horrifying and nigh-unimaginable.[/li][li]Therefore, unintended consequences (like AGW) cannot be believed to exist.[/li][li]And Magical Thinking is assumed on some level to work, just like praying away disease. (The only people who get sick are those to want to be sick, or something.)[/li][li]And of course Socialized Medicine is just as offensive to a “Christian Scientist” as public funding of abortions is to a Catholic.[/li][/ol]
Now, it’s not just Christian Scientists. Racists get their nods in policy platforms, Catholics get to see public schools defunded, Baptists get lip service to the idea of prayer in schools (or vouchers for their own sectarian schools), and presumably some proportion of evangelicals are voting for a belief in weird *anti-government *conspiracy theories.
The fact that this involves playing to a bunch of wacky religious biases that are historically arrayed against each other, and encourages balkanization, doesn’t seem to stop it. On the contrary, the GOP is essentially using its constituents hatred of each other–of other GOP voters of the wrong faith–to keep the persecution complex going.
All in a “Nixon was right” culture. 
But, you know, I may be making all that up. I sound like a character in* Illuminatus!*