They [Jewish people] benefit from the same institutional racism as white people, hold the same position of privilege, and—actually—look down on all gentiles, yet every time you mention this you’re instantly painted as anti-Semitic.
Jewish people are considered white people, but Jewish people can also experience anti-Semitism. Just as a white, gay man can be called white, he can also be harassed for being gay. The issue is entirely contextual.
I don’t think there are many Jews who would claim they have it worse in America than black people.
Adding to this, in the United States, ‘whiteness’ is a concept that expands and contracts as needed, always at the exclusion and in opposition to people identified as ‘black’. Italians and Greeks and Slavs are white now when, 100 years ago, to be white was explicitly in opposition to those groups.
Those groups have been allowed to escape from targeted discrimination and, in fact, now benefit from it.
For ethnically Jewish people, the racial trajectory has been similar, and, as a religion, Judaism is close to (white) Catholicism and the LDS church in being considered ‘Christian’. In the past, only some variants of Protestant were accepted as orthodox in its broadest sense, but now there’s space to include more.
New targets of hatred and otherness allow some past examples of ‘Them’ to join in the ‘Us’. In the current moment, Muslims of all kinds and Mexican and Central Americans are the enemy, along with black people as always, and the latest queer group to assert itself: trans people.
Queerness works in a similar way but always on the frontier, strengthening the defenses of marginalized communities rather than working to consolidate a powerful majority at the expense of others. That’s the bargain of whiteness. You don’t materially improve your condition absolutely, but you are able to improve it relative to someone else. You don’t necessarily get a better job, but you might be able to keep someone else from getting a better job, so you have a bit more security where you are.
Jewish people are in a position like gay men where, in some parts of the country, they’re still going to be discriminated against and regarded with suspicion or hostility, but if they can ‘pass’, they’ll be just fine. A masculine-acting gay man who’s white and cis like Peter Thiel might just be able to go through life with people assuming he’s straight, so he can enjoy the privileges associated with that. A Jewish person with a German-sounding name and no accent gets all the benefits of a default reading. Put those people in a rural area, especially in the Deep South but also West and Midwest and Southwest, then pervasive prejudices become more pronounced because they’ve survived in small, isolated towns like some sort of bigoted shibboleth.
To get at your question more directly, criticisms of white people and white supremacy tend to include Jewish people now that Jewish people also benefit from structures of white supremacy, even if in the past, some of those structures were erected in opposition to Jews. However, specifically Jewish criticism is not considered acceptable because it draws on historically antisemitic language, reasoning, and arguments that are spurious and dangerous.
A Jewish person regarding themselves as a member of God’s chosen people in the United States or Europe is not an especially dangerous idea because they don’t operate the levers of power in society by virtue of their Jewishness.
This thought may be dangerous in Israel, however, because people there do wield power with consequence based on the idea that a Jewish state should be for Jewish people and everyone else is something less than fully human or deserving full human rights and dignity.