It's important to note Evangelicals largely supported Carter in 1976, and only became the Religious Right after Reagan made them Republicans - so losing to Carter isn't the death blow a, say, Ford '76 TL would be. The GOP right-wing hasn't really been beaten down, just dealt a setback. Nixon and his One Nation-esque ideology have already been discredited, and there's the question of how the Fordist model does in '84 - I doubt Ford himself runs, seeing as the only consideration he saw in 1980 IOTL was with the possibility of the convention deadlocking and that possibility quite quickly died. And Agnew is politically dead - he can deny it to his dying breath no one recovers from taking a bribe on White House grounds, especially if they pled guilty to it.
I think the natural evolution of the GOP is still heading in the right-wing but with less supply-side economics, though Reagan not murdering any chance the Fordist wing had at being a co-equal faction of the GOP instead of being completely squashed will mean this is not an unchallenged right-wing like IOTL. And this will run up against the fact that the religious right and cultural right both, eventually, still likely migrate into the GOP, but without Reagan at the head their faction is not being totally unopposed. Vidal said in the very first post of this thread this is not a liberal utopia, so the GOP is unlikely to see anything happen to seriously avert its right-wing shift, but more likely simply see a different flavor of right-wing shift.
As for who wins in 1984 - if the economic conditions are good and the GOP has a nasty nomination fight/the GOP nominates a Dukakis-level campaigner, Mondale (who almost certainly has the Dem nomination if he wants it) could very well win, but I lean more towards the GOP narrowly beating Mondale with whoever they nominate - it's more in line with the IRL examples of 1960, 1968, and 2000, where 1988 really seems the exception that proves the rule. And there's no guarantee the 1983-1984 boom of OTL happens ITTL, depending on actions from both Carter and Volcker, and if it isn't happening then Mondale's chances, while still not horrible are less good. The GOP nominee is an open question but while they could be right-wing they won't be a supply-sider, as Reagan's loss probably does discredit that specific element of the Republican Party (and the whole 1980 debacle, plus the fact the highest office he's held is U.S. Representative - which has a very poor, if not non-existent, record at winning the presidency - means Jack Kemp is very, very unlikely to be the GOP nominee in 1984).
