The tensions at the 2016 Republican National Convention aren’t like those typically seen at the party’s divided gatherings: Teddy Roosevelt challenging the hierarchy in 1912; or the moderates versus conservatives, Dwight Eisenhower against Robert Taft in 1952, or 12 years later, Barry Goldwater and Nelson Rockefeller, then Ronald Reagan taking on President Gerald Ford in 1976.

Republicans meet in Cleveland on Monday to anoint their presidential nominee amid deep schisms: Never have so many of the party’s prominent governors, senators, House members and, most conspicuously, former pres...