American conservatism is having something of an identity crisis. Most conservatives supported Donald Trump last November. But many prominent conservative intellectuals—journalists, academics and think-tank personalities—have entrenched themselves in bitter opposition. Some have left the Republican Party, while others are waging guerrilla warfare against a Republican administration. Longtime friendships have been ended and resignations tendered. Talk of establishing a new political party alternates with declarations that Mr. Trump will be denied the GOP nomination in 2020.

Those...