It strikes me that the best criticism of the order is that the executive branch is expanding the reach of Title VI, and has been since the Bush II administration, without either Congressional action or at least a formal rulemaking process that would allow public objections during the notice-and-comment period and also litigation against whatever winds up being published in the Federal Register. As someone who was strongly critical of the Obama administration for governing through executive order and informal guidance, I'd need some persuading as to why the same criticisms don't apply here.
As for measured substantive criticism, David Schraub in The Atlantic provides a useful and thoughtful summary of criticism from the left. Here are some of the prominent criticisms, and my response.
(1) While there is nothing inherently wrong with the Trump executive order, Schraub suggests that Jews and others rightly don't trust the Trump administration regarding antisemitism, and therefore don't trust the administration to properly and fairly enforce the order on college campuses. Whatever one thinks of Trump and his administration–and I have knowledgeable Jewish friends who think everything from 'the Trump administration is institutionally antisemitic' to 'the Trump administration is the most philo-semitic in history'–it's not the "Trump administration" that enforces Title VI, it's the Department of Education Office for Civil Rights. There's no reason to think that the civil servants at OCR have gone Trumpian. Ken Marcus, the political appointee who runs OCR, has made a career out of fighting antisemitism; it's ridiculous to think that Ken deserves Jews' mistrust.
(2) Shraub references the "more legitimately controversial aspect of the Executive Order: its misappropriation of the IHRA definition of anti-Semitism for use in assigning civil liability." Schraub fails to make it clear that this definition is only to be used as possible evidence of discriminatory intent when otherwise potentially illegal discrimination is going on. No one is going to be civilly liable for saying something that violates IHRA by itself. True, aggressive bureaucrats can blur this distinction under hostile environment law, and ignore relevant First Amendment constraints. But that's a problem with hostile environment law and aggressive bureaucrats, not in using the IHRA definition as one factor in assessing discriminatory intent. I'm all for constraining hostile environment law with strong First Amendment protections, but I'm not in favor of the position that hostile environment law should be applied vigorously to protect other minority groups, but not Jews.
(3) Finally, Schraub suggests that the Trump administration has proven itself all-too-willing to crack down on speech on campus related to the Middle East it doesn't like. In particular he objects that the Trump administration has violated freedom of speech and academic freedom by starting to monitor academic balance in Middle East Studies programs that receive federal funds. I certainly agree, as a general matter, that the federal government has no business monitoring academic programs for balance. But the particular funding program at issue provides funding for Mideast studies to promote knowledge of the Middle East to serve U.S. foreign policy objectives. As a result of this mandate, the relevant funding law requires universities to pledge that their programs will be balanced. In other words, monitoring balance is not some bizarre or aggressive anti-academic freedom initiative, but just enforcing the law–a law, admittedly, that previous administrations failed to enforce. But aren't we having an impeachment right now in part over the notion that the executive branch is supposed to follow Congressional mandates with regard to appropriations? Universities should not accept money with such strings, especially when the money is not, as it is not in the Mideast Studies funding context, remotely crucial to their fiscal stability. But if they do accept federal money with such strings, they, and critics like Schraub, can hardly object that their academic freedom is being denied.
UPDATE: How might the IHRA definition of antisemitism be used as evidence of discriminatory intent? Imagine a university administrator who refuses to give a room reservation to a black student group. He claims that it was just a bureaucratic error, not discrimination. But he sent a note with the denial with a tagline "white lives matter." It's not illegal to say "white lives matter." But it can surely be evidence of discriminatory intent in that context. Similarly, Hillel, the Jewish student organization is denied a room reservation. Same scenario, but the tag line is "Zionists are Nazis." It's not illegal to say that. But it can surely be used as evidence that the Hillel room reservation denial was motivated by discriminatory sentiment against Jews, and it would be almost facetious in that context to say that the tagline was merely evidence of hostility to Israel and its supporters and not evidence of discriminatory animus toward Jews.
David Bernstein is the University Professor and the Executive Director of the Liberty & Law Center at the Antonin Scalia Law School, George Mason University.