So, is there any future for the Republican Party, or is it doomed for a very long time to come? Will it be replaced by something new? Any thoughts?
it's fine - what's going on in the US right ow politically isn't new, and the next 100 years are completely predictable.
It would be hard to be as precise as the psychohistory of Isaac Asimov's Foundation series, but overall, that is likely correct unless advancing technology makes a lot of social hierarchy unnecessary.
human history's default starting point was tyrants and oppression, and over 3000 years has been a long repeating sequence: progressive periods with gains to human rights and improvements to the human condition, followed back a regressive backlash trying to reinforce oppression.
in the US the last big progressive push finished up in the early/mid 70s and the social pendulum has been swinging in the other direction ever since - the US has been on a cultural conservative slant for the last 40 years with relatively little progressive social change.
i would guess it will be 15-30 years before this regressive period is over, so the GOP is going to be completely fine for that long at a minimum. the republican party is serving the values and political desires of their constituents quite well right now, so the party is in a very healthy place. ...
Cyclical theory (United States history)
Arthurs Schlesinger I and II proposed that sort of theory of US history, an alternative between liberal and conservative phases, public purpose and private interest, increasing democracy and containing democracy, concern with the wrongs of the many and concern with the rights of the few, human rights and property rights.
Conservative phases end from unsolved social problems not being addressed by society's elites. This provokes activism to solve them, activism that produces a liberal phase.
Liberal phases end from society-scale activism burnout and from changes being a bit much to digest all at once. Wanting a rest produces a conservative phase.
Another cyclic effect is party systems, sets of characteristic platforms and constituencies for the parties. Also Stephen Skowronek's political-time cycles. Each cycle starts with a reconstructing President, one who leads an overthrow of earlier political paradigms and creation of new ones. His party then becomes the dominant party, with the other one becoming the opposition party. He is succeeded by Presidents in his party, articulating Presidents who expand on the era's political paradigms. He is also succeeded by opposition-party Presidents, preemptive Presidents who try to oppose those paradigms, typically without much success. Each era is ended by one or more disjunctive Presidents, Presidents who try to keep failing paradigms going.
Other big events are Samuel P. Huntington's periods of "creedal passion". According to him, "In terms of American beliefs, government is supposed to be egalitarian, participatory, open, noncoercive, and responsive to the demands of individuals and groups. Yet no government can be all these things and still remain a government."
Also periods of race-relations upheaval, periods that cause great national trauma.