If the GOP loses christian evangelicals , other republicans won't pretend to believe in YEC (from which derives lots of anti-evolution sentiment) and personhood at conception, as much
. However, I think birth control has a lot of complexity as a moral issue (a maybe baby's rights vs the mother rights and, if you're into authoritarianism, society's gain), so it's not going to be much less important just because a former hard-line left. I think the GOP just hangs onto these kinds of devout christians, because you basically need national approval and support to have political success, even on local levels. Perhaps the GOP could schism in such a way that that group starts voting more like African-American religious so-cons. That'd be really strange though.
Global heating is just obnoxiously political, I basically ignore any politician who brings it up. The whole conversation should be academic, because nothing short of a totally authoritarian government could stop people from using IC engines (runnen' off moonshine if gasoline isn't refined anywhere) and hydrocarbon powerplants (ie generators if it's illegal to use central powerplants). The big names in global warming travel by jet and live in mansions, ffs. As a culture, we're addicted to energy (I'm not complaining!) and the buzz is just soooooo good. I hope we ride the buzz into fusion and (non-crony) renewables before we start getting supply scares on coal and natural gas. The best we can do is help our neighbors past as much dirty/destructive technology as we can and make all material goods as efficient as possible. With sufficient technology, the only global heating we need to worry about is from waste heat.
Anti-vaccination seems to be fairly bi-partisan, though I think it's a pretty uncommon position in general. The general argument is just based on ignorance of disease and of science. The libertarian argument makes me sad, because vaccines are quite safe and prevent so much suffering. Requiring them is immoral, but I can't help but be a dirty pragmatist about it.