"As a Dem/Prog. which GOP candidate would you support?"
This is actually a response republicans and conservatives should pay close attention to, given the fact democrats, moderates, and independents will determine who the next president is.
If republicans seek out the 'most conservative' candidate for president they can find, then they've already lost the election.
Yes, republicans have the right to nominate whomever they wish, to reflect their dogma and agenda, including a hard-core, extreme rightwing agenda, provided republicans understand that a majority of the voters will reject any republican candidate who advocates such an agenda.