It was difficult to miss Ian Jacobson at the Conservative Political Action Conference. Known as Rooster, he was 33, with an ample beard, earrings and a towering orange-and-aqua spiked Mohawk haircut. But he also sported a pinstriped suit, French cuffs and a natty contrast collar. Mr. Jacobson’s sartorial contradictions matched those of his politics: He is among the young Republicans who are pro-free market on fiscal issues and libertarian on social ones. While his views represent a potential growth wing for a party that is losing among other demographic groups, they also show an emerging tension with the older social...