And some 800 miles away from Gainesville, administrators at the University of Cincinnati, who also received a request for Mr. Spencer to speak on campus, eventually agreed to negotiate a date in mid-March during the school’s spring break. Last week, a lawsuit filed in federal court accuses the university of excessive and therefore “unconstitutional” security fees for Mr. Spencer’s appearance. The amount: $10,833.

The University of Florida would eventually cancel Mr. Spencer’s visit, but not for long. Mr. Spencer, a leader of the far-right white nationalist movement, had the law on his side. When it became clear that his visit was certain, the administration coordinated an event that would come to include a $600,000 price tag. More than 1,000 police officers converged on the ground, in the air, on the roofs — and there was plenty of soul-searching about the role of public universities as incubators of ideas, even those that are unpopular.

“Fear and dread. I just kept thinking, the same person who was in Charlottesville is now coming here,” said Mr. Fuchs, who became president in 2015. “Before, this was about rhetoric, now it was about violence.”

The Florida event did not go without some violence. A self-labeled white supremacist was sucker-punched while wearing a swastika T-shirt (he was later hugged and befriended by two black men) and three Texas men were arrested and charged with attempted murder after they taunted a group of anti-Spencer protesters after the event. One of them fired a shot, missing the group.

“It’s not just about the speech,” Mr. Spencer said. “It’s about the demonstration of our resolve, of the power of our ideas, of the fact that everyone now has to have an opinion on them.”

The National Policy Institute, led by Mr. Spencer, first requested a rental space on Florida’s campus on July 31. The university had already agreed to a Sept. 12 date and a campus location when Charlottesville erupted.