The Republican party seems to have gone full death-cult.
I am not sure in what sense you mean this. If you mean in the sense that the party is taking actions that will lead to its own extinction, well, maybe. But . . .
And yet people will vote for them, no matter what they do.
I'm not sure I'm onboard with that one. No matter what they do, they will get some votes, but they will be from different people, depending on what they do. At present, there is a Democrat in the White House, and Democrats control both the congress and the senate, so if there are people who vote for Republicans no matter what they do, there aren't enough of them to keep the Republicans in power.
A moderate Republican tends to do reasonably well in general elections, but a hard-right Republican tends to beat the moderate Republican in primary elections. Ask any Republican in congress, of whom they're afraid - their answer may well not be the democrats. It is often that, if they are deemed insufficiently conservative, they will face a primary challenge from someone claiming to be a "true" Republican, instead of the Democrat in disguise, or the "RINO", or whatever derogatory term they are using for insufficiently "conservative" Republican candidates.
At the presidential level, here are the people who have run since 1980:
1980 - Ronald Reagan - won
1984 - Ronald Reagan - won
1988 - George H Bush - won
1992 - George H Bush - lost
1996 - Bob Dole - lost
2000 - George W Bush - won (although lost popular vote by relatively narrow margin)
2004 - George W Bush - won
2008 - John McCain - lost
2012 - Mitt Romney - lost
2016 - Donald Trump - won (although lost popular vote by relatively larger margin)
2020 - Donald Trump - lost
So let's look at the Republicans who lost - George H Bush (in 1992), Bob Dole, John McCain, Mitt Romney, Donald Trump (in 2020).
If you ask me, apart from Donald Trump in 2020, that's the list of the more moderate Republican candidates. (You could make a case for Reagan being "moderate" by today's standards, although he would have been considered pretty conservative in the 1980s.)
How about those who won - Reagan (twice), George H Bush (in 1988), George W Bush (twice), Donald Trump (in 2016). The only one who wasn't "hard-right" by the standards of the time was George H Bush.
So, if you look at hard-right and moderate Republican presidential candidates, there's a pretty strong correlation (when you classify them the way I do) with winning and losing. If you classify them as "hard-right" or "moderate" differently than I do, you might reach a different conclusion.
The senate tends to be more moderate than the congress, because a candidate has to appeal to the whole state rather than a single district (the exception being the small states, where the district is the entire state). So there's a reason why you tend to see relatively more nut jobs (and not always Republican ones) in the congress than in the senate. But the congress is where the big danger for Republicans is not the Democrats (most of the districts are gerrymandered to be relatively "safe" for one party or the other), but the within-party challenge from a more conservative Republican. To take a hypothetical example, how would Arnold Schwarzenegger do if he ran for congress in Orange County? The place was a Republican stronghold for decades, then Democrats did a clean sweep of the congressional seats in 2018. If there is a Republican who can beat Democrats in California, Arnold Schwarzenegger just might be that Republican. But can he beat more conservative Republicans in a primary election? He won in all of California, but how about in Orange County?
So it seems there is a balancing act. The more right-wing and wacko you are, the more likely the Republican base is to support you (not all of them, there are plenty of Republicans who hate the extremists - just not enough of them). But the more wacko you are, the less likely you are to appeal to swing voters. In congressional districts, the swing voters don't matter that much, because everything is gerrymandered. But in presidential elections, my judgement is (and we are working off of pretty limited data, there is only one election every four years) that appealing to the wacko vote gains you more than it loses from the non-wacko centrist vote.
