The gunman responsible for a shooting at a Chabad in Poway, Calif., said he was inspired by Adolf Hitler’s ideology. Robert Bowers, who killed 11 in the Pittsburgh massacre, posted anti-Semitic messages on the social media platform Gab, popular with white supremacists and the alt-right. Blaze Bernstein, a gay Jewish University of Pennsylvania sophomore, was murdered near his California home in January 2018, and the suspect awaiting trial is a known neo-Nazi.

The threads tying much of the anti-Semitic violence to white nationalist ideology are impossible to ignore. Those seams grew ever clearer in Charlottesville, at “Unite the Right,” where demonstrators displayed swastikas on banners and shouted slogans drawn from Nazi ideology, like “blood and soil.” When white nationalist Richard Spencer was interviewed about the role of anti-Semitism at the rally days later, he said Jews are overrepresented on the left and establishment as “Ivy League-educated people who really determine policy” while “white people are being dispossessed.”

The president himself has trafficked in anti-Semitic stereotypes, frequently endorsing crude, negative caricatures about Jews. On Saturday, speaking before the Israeli American Council, Mr. Trump said that Jews should support him because Senator Elizabeth Warren’s wealth tax would put them out of business.

“A lot of you are in the real estate business because I know you very well, you’re brutal killers,” the president said. “Not nice people at all, but you have to vote for me. You have no choice.”

Criticism of the president’s executive order has come from across the ideological spectrum. The Foundation For Individual Rights in Education, a group that advocates free speech on campus, often for conservatives, said the executive order would “impermissibly threaten the expressive rights of students and faculty at institutions across the country.”

Senator Brian Schatz, a liberal Jewish Democrat from Hawaii, summed it up: “The idea that a college campus would have its views on Israel regulated by the federal Department of Education? Oy Gevalt.”

Mr. Trump’s executive order points agencies to the definition of anti-Semitism prepared by the International Holocaust Remembrance Alliance. This definition includes several examples of speech that should be covered by the First Amendment, like “claiming that the existence of a State of Israel is a racist endeavor.” For this reason Kenneth Stern, the lead author of the definition, wrote in The Times that it shouldn’t be applied to higher education. The agency’s definition was prepared for data collectors writing reports in Europe, not for government officials policing campus speech.