As Donald Trump emerged victorious in the race for the Republican presidential nomination this week, the loudest cries of anguish heard in Washington may well have come from one section of his own party—from those in its conservative movement.

“Conservatives had their party hijacked from them in the 2016 primaries,” wrote Jonathan S. Tobin in Commentary, a leading platform for conservatives. He added: “The consequences for individual liberty and restraint of government power, not to mention America’s foreign-policy interests,...