“We’d like to have a hand in helping the President by giving him an avowed socialist to face in November!” the organizers of one of the groups, Trump 2-29, a reference to the date of Saturday’s primary, wrote on its Facebook page. “Haven’t you waited a VERY long time to DO SOMETHING for President Trump??? Here ya go.”

The organizers conceded that they relished the chance to roil Democrats, especially during a moment in the campaign when friction between the party’s candidates has become especially acute.

But they said they were motivated by a larger mission: For years, conservative activists have sought to close South Carolina’s open primaries, and this election offered ideal circumstances for creating a live demonstration of the flaws they see in the system.

“We were also looking for a way to get Democrats to support the cause of closing the primary,” said Christopher Sullivan, a longtime critic of the open primary and leader of the Conservative Defense Fund, a small advocacy outfit in South Carolina. “And this is a way of showing them what’s good for the goose is good for the gander.”

Charges of “party raiding,” as the tactic is known, have been leveled repeatedly over the years from both parties, in presidential races as well as down-ballot statewide legislative contests. Still, experts said, evidence of these efforts achieving any sort of significant influence is hard to find.