It was pitched as the world’s most exclusive invitation. Hundreds gathered at President Trump’s private country club in Virginia in May for a gala evening. Guests included Justin Sun, a cryptocurrency billionaire who, in the Biden administration, was under investigation for suspected financial crimes. He and the other attendees had won their seats by being the top buyers of $TRUMP memecoin, a form of crypto that benefits Mr. Trump’s family. “There is a lot of common sense in crypto,” said Mr. Trump, as the room was served a meal accompanied by Trump-branded wine and water. “And we’re honored to be...