Libertarians picked Trump to headline their convention. Then an internal revolt erupted.

Some Libertarian Party leaders are fuming over the party’s decision to have former president Donald Trump headline their national convention this month, with national committee members calling on the party to rescind the invitation.

The choice to have the presumptive nominee from another party speak at the Libertarian Party’s nominating convention has inflamed growing schisms within the minor party. State and local factions, presidential candidates and critics of the right-wing caucus that controls the party are registering their anger with Trump’s planned appearance. Over the weekend, the party’s leadership debated disinviting Trump from the convention after the treasurer...