The American political system, indeed everything about America including the amount of money required to start a real third party, is infinitely larger and more complicated than was the case 150 years ago. So your 10th-grade civics class-level analogy is largely irrelevant.
I don’t “blindly” support the GOP. I support it with my eyes open. My open eyes tell me it’s still far better than the Rats. In addition, moving the GOP in the right direction, while desirable and necessary, is not necessarily accomplished by conservatives leaving it. You assume the party leaders will respond to this hemmorhage in good ways. They might also respond in bad ways. Furthermore, moving the party in the right direction is not as important as keeping the Rats out of the White House AND winning back Congress.
While they're *both* important, keeping the RATs out is motivation #1 for me.