It would be fascinating if any of these major right-wing states ever actually left the union. Picture what would happen in Texas did, and managed to negotiate a peaceful exit. That would immediately subtract 38 electoral votes that reliably go Republican, making winning the presidency extremely difficult for any Republican. It would also make it harder to win either house of Congress. And assuming the exit settlement allowed for some movement of people prior to secession, it would be even more extreme than that. A lot of minorities and liberals in Texas would see the writing on the wall and get the hell out of Texas before they wound up prisoners of a wingnut Republic. Meanwhile, some of the hardest-right people in other states would relocate to Texas. There's a good chance the net movement would be enough to push a couple states (FL, NC, OH?) from the red column to the blue one.
Of course, things would be more complicated than that, since if Texas left, some others might, as well. It's hard to see Oklahoma and Arkansas sticking with the Union instead of the neo-confederates in Texas. That would push things even farther left in the remaining nation, to the point that a politician anything like the current batch of Republicans would have no chance of winning the presidency, and anything like the current GOP would have no chance of winning either house of Congress. And, of course, with that realization, it would be hard to stop red states in general from going with TX.... along with a massive brain drain going from there to the blue states.
So, it's tough to see TX leaving without it being part of a total unwinding of the US into two major blocks.