In some ways, they are a typical political power couple seeking to “Make America Great Again.” They are throwing a $5 million fund-raiser for President Trump this winter, and are quick to make it known that they have the president’s sons’ cellphone numbers on speed dial. They have poured more than $50,000 of their own money into supporting the president, who smiles in photos on the bookshelves of their home. But Bill White and his husband, Bryan Eure, are not red state evangelicals or die-hard right-wingers. In fact, for years, they were key players among a cohort that Mr. Trump...