What the GOP needs to do to stay relevant federally is represent their state or constituence well, move federally to a right wing populist platform similar to their European variant, but become more secular, supporting realistic ways to deal with climate change but not deny it, focus on supporting rural and working class areas and small / local businesses. Making sure economic growth is felt over all regions, not just metropolitian areas and decide controversial issues on a regional level like abortion and death penalty. Let the regions decide. With competent leaders they would keep many states in the red column because many people will never ever vote blue and win the rust belt + mn + nh + me and maybe only lose az and in the long run ga + fl. TX however has potential to rapidly shift in the blue column.
The way they would "deal with climate change" would be to say its better policy to build prepare for instead of trying to prevent it with a few moderates on both sides saying we need to deregulate and subsidize nuclear power and fusion research.