Despite strong pressure from the Trump administration, including a call with the White House on Friday, colleges and universities are largely rejecting the president’s offer of preferential treatment for funding in exchange for compliance with his ideological priorities. Six of nine universities offered the deal earlier this month had publicly said no to the White House request by Monday’s deadline for responses. On Monday, the University of Arizona and Vanderbilt University did not accept the deal, but said they were open to more discussion. The administration has said it is seeking to make sure the country’s schools are merit-based, but...