I might have completely nonrepresentative acquaintances, but the young Republicans I know are mostly evangelical Christians, and definitely not apathetic on social issues. They are however more socially liberal than older evangelicals on certain generational issues; e.g. you won't find many people under 30 who want to re-introduce laws criminalizing sodomy.
edit: And actually on the flip side, I'm not sure they're fiscally conservative. Compared to older evangelical leaders who strongly support the Reagan-era evangelical/business-conservative-alliance, among the younger generation there seems to be more skepticism of markets, and focus on poverty/inequality as issues.
I would also note that there are plenty of social regressives/fiscal apathetics who call themselves "libertarian" because it doesn't have the stigma of "Republican".