Republicans would lose SOME support from the evangelical and Southern White voting blocs, but I think enough of them have bought into fiscal conservatism over the last few decades, plus a more libertarian GOP would still be conservative on the issue of gun control, so I think enough would stay to not necessarily lose that many states. Democrats would likely go back to a New Deal era approach of focusing on propping up the middle- and working-classes. My best guess for a 2024 election between Brian Sandoval and some fiscally progressive Democrat who focuses more on "fiscal populism" than they do on wedge social issues:
A loss in some support from working class Whites in Georgia, Louisiana and Mississippi combined with steady Black support flips those states. Arkansas, Kentucky and West Virginia return to voting based on their economic interests. Upper New England "comes home" to the Republicans. The Pacific Northwest is the closest region, with the GOP winning over just enough swing voters in the suburbs of Portland and Seattle to carry those states.