John David Rice-Cameron can trace his conservative roots to his middle school years. Back then, his father would often have talk radio on during rides home from school or tennis practice. “Sometimes my dad would listen to Rush Limbaugh and he would kind of argue with him,” recalls Rice-Cameron, 20, a sophomore at Stanford University. “I just found myself agreeing with basically everything Rush Limbaugh was saying.” Rice-Cameron’s parents are Democrats. His mother, Susan Rice, served in the Obama administration, first as U.N. ambassador, then as National Security Advisor. But despite his parents’ political leanings, “they believe extensively in debate...