The concept of "Jewish Privilege" is one of those concepts that flits between the far-right and far-left (Rania Khalek tried to promote it amongst leftists, but David Duke (link alert) beat her to the punch). It has a deep antisemitic pedigree, which makes it alarming to see it starting to creep into the discourse of liberal Jews who should know better (Peter Beinart and Mira Sucharov). Whatever we might think about the ways Jews are advantaged by certain Israeli policies, the term "Jewish Privilege" is inextricably bound up in a history of trying to get Jews killed. It should not be used.
As if to illustrate the point, several flyers at the University of Illinois-Chicago make quite explicit the attempt to leverage the concept of "Jewish Privilege" as a means of fomenting a left-right alliance against the Jews. The theme of the flyers is that battling "white privilege" is really about battling "Jewish privilege", where Jews are cast as the real beneficiaries of illicit social gains. The flyers contend that (a) Jews are the predominant members of the "1%", (b) Jews are vastly and illegitimately overrepresented at elite universities, (c) Jewish donors are responsible for the "unhiring" of Steven Salaita at the University of Illinois, (d) one is allowed to "question" everything but the Holocaust, and (e) Auschwitz and Gaza are identical. They conclude by asserting that raising these points is not "antisemitic" or "insulting" or "defamatory", but "social justice" or a "human right" -- and conclude by adopting several putatively leftist hashtags (e.g., #BlackLivesMatter or #WeAreAllMuslim).
My instinct is that these are far-right efforts to attract support from leftist groups to antisemitic causes (though honestly, these are the sorts of endeavors to which the Universal Extreme Left-Right Convergence Theory applies). I have seen condemnations (and disavowals of responsibility) of these flyers from various left-wing groups that are implicated by the hashtags (here's BLM Chicago, and I saw a separate statement by various leftist UIC campus groups that was circulated by email but not posted online).
But again, the ease in which this sort of rhetoric is appropriated to obviously antisemitic ends should rightfully give pause. The arguments made in these flyers are not, unfortunately, that far off from ones that one does see percolating in leftist spaces -- from demands that we interrogate excessive Jewish power to vicious comparisons identifying Israel with Nazis. Efforts to craft collaborative left-right antisemitism don't come from nowhere. They come because the antisemites know fertile ground when they see it. That doesn't make the condemnations less welcome. But it does suggest that there is work that needs to be done beyond the issuance of a press release.