It doesn't strike me so much as a question of the Republican party evolving all on its own, but rather why the US public rewards an ongoing movement rightward which is the basis of the current party--conservative and conservativerer. That would not be the case if electorates did not keep voting in politicians who try to top the conservativeness of their predecessors.
In another GeographyDude thread that everyone else seems to be ignoring, I argue that what calls itself "conservative" in the post-Reagan era in this country is inherently in bad faith, newspeak for rule by a privileged oligarchy. But so it could be argued is modern "liberalism" which in fact tries to avoid even that milquetoast label and call themselves "moderates" instead. Basically what I see is that the rational self-interest of the vast majority of Americans lies far to the left of what they seem willing to vote for.
Now I also think that the modern electoral battlefield is effectively rigged, by gerrymandering and most inherently, by the winner-take all electoral system. But even with a corrupt and winner-take-all system an insurgent leftist program should be able to get into power if enough Americans support it.
Well then I might just be nuts and crazy to think things should be moving in the opposite direction or anyway should stop moving any farther right, but I meet just enough people who agree with me on many points that I think, no, it is not that we Americans really all want this right wing craziness, it is that the majority is effectively immobilized, voiceless, and brainwashed and above all discouraged from effective action. We can't think straight because we are lobotomized, I suspect.
The notion that maybe I'm just some over propagandized outlier has been glumly with me most of my adult life, but then along came the Sanders primary campaign of this year to demonstrate that these same "crazy" left wing notions I have are in fact shared by millions of small business owners and military veterans across the nation.
So the question is not, "why are Republicans so far to the Right," but how come the United States as a whole is?
Nor is it "why aren't the Republicans all unified in some consensus on just how far right they want to be?" Obviously there is going to be a spectrum. The question is, why is the spectrum centered so far to the right, and getting more so in rhetoric every decade?
Related to this, probably much more germane than "why do the Republicans do as they do?" is "how come Democrats can't shift the center back leftward again?"
If we accept the Republican world view that all the countries of the world, even the USA, have been too far to the left all along and things would be better the more we get rid of what Americans call "liberalism," then it is only rational that the Republicans would be deployed as they are--but then the question is, why didn't they accomplish their goals back when George W. Bush presided over a House and Senate all controlled by his own party? Which he had for six years after all. I think the answer is clearly "every step we take to the right is disastrous and obviously so, so Bush tiptoed." Enacting any of the major platform planks would erode their support very rapidly, unless democracy were openly done away with. Which I suppose is always a possibility, but it has costs. What I regard as the true driving force behind modern American "conservatism," plutocracy, is well served by the current quagmire where Democrats and Republicans are entrenched on current terms and at loggerheads, jamming any grand policy and causing changing policy to happen in little uncoordinated increments, while private power continues to grow more and more entrenched and normal-seeming.
It would not do for the Democratic party to drift leftward without let or hindrance because in that direction, more or less, lies a viable program for populist democracy that is prosperous. But since the reaction to that is not reality based, it can spin its alternate rhetoric in ever more hyperbolic terms all it wants to; the programs will be enacted only to a limited and selected degree, and will do little harm to the tiny fraction of the population that has enough wealth to "matter." The rest of us are expendable.