In the minds of many moderate American voters, and certainly the political class in Washington, the Republican Party has a big problem: Whenever it seems to have figured out a formula for success, uncomfortable debates over so-called social issues raised by party-base activists seem to get in the way. In 2012 and 2014, it was the Republican Party’s supposed fixation with contraception. More recently, the issue du jour has been gay marriage. Buying into the theory that active engagement on these issues is a losing battle that will do more harm than good, the Republican leadership has tried to avoid...