Trump's executive order on anti-Semitism deserves severe criticism - but not for the reason most people have focused on:
The main objection people raise is that it apparently defines discrimination against Jews as being based on "national origin," which critics argue is inaccurate (because Jews are actually a religious group), and may even amount to prejudicial classification of Jews akin to the Nuremberg laws. It's also possible to interpret the order as defining this type of discrimination as discrimination based on "race" - though I doubt that interpretation would mollify critics.
Many people who consider themselves Jewish and/or are perceived as such by society are defined that way based on ethnic background, not religion. Thus, there are numerous Jewish atheists and agnostics.
In reality, much modern anti-Semitism is in fact based on ethnic/nationalistic considerations rather than hostility to the Jewish religion. This is true of most modern right-wing anti-Semitism dating back to the 19th century (Nazi anti-Semitism is the most notorious case, but far from the only example).
Most modern left-wing anti-Semitism is also primarily focused on supposed ethnocultural characteristics of Jews, rather than religion (e.g. - claims that Jews are greedy capitalists who only care about money). This is what's behind the famous saying that "anti-Semitism is the socialism of fools."
Anti-discrimination law generally focuses on discrimination based on perceived ethnic or racial characteristics, not on whether the victim "really" belongs to the group in question. Thus, if someone discriminates against someone based on their perceived "Jewishness", it would not matter that they are not considered Jewish under Orthodox Jewish religious law. It would not even matter whether they consider themselves to be Jewish.
The real problem with the Executive Order is the extremely broad definition of anti-Semitism, which threatens free speech. See the FIRE statement linked below (FIRE is a leading advocate of free speech on campus).
https://www.thefire.org/fire-statement-regarding-executive-order-on-campus-anti-semitismHow bad it will be may depend on how it is interpreted by various federal bureaucrats and university administrators. To put it mildly, neither group has a great record on such issues. Moreover, the very fact that it comes down to this kind of bureaucratic discretion can itself chill speech.
While much, probably most, anti-Zionism is in fact thinly disguised anti-Semitism, this definition covers any speech denying "the Jewish people their right to self-determination." Thus, it includes even those who reject all claims to "self-determination" based on race, culture, or ethnicity (FWIW, I take the same view of ethnicity-based claims of other nationalist movements, including Palestinian ones). And, of course, even genuinely anti-Semitic speech is protected by the First Amendment.