Answer: Both (frequently) detest the Jews.
Jacobin Magazine has a fascinating and thoughtful article by Landon Frim and Harrison Fluss on the curious case of Jason Reza Jorjani, a recent Ph.D. recipient from the ultra-lefty SUNY-Stoney Brook philosophy department who is now one of the major house philosophers of the alt-right. The article is primarily a critique of the anti-enlightenment tradition within philosophy (often associated with "Continental" philosophers) which, despite its often superficially progressive garb, the authors contend is and has been easily coopted and appropriated by the far-right. Jorjani, for example, doesn't draw just from the usual right-wing suspects (Heidegger, of course, was himself a Nazi) but from sources viewed as unimpeachably liberal like American pragmastist William James.
One thing the piece does is provide outstanding detail on just how the anti-enlightenment project has, historically, by justified by and gone and hand-in-hand with hatred of Jews. Opponents of the Enlightenment and its values were relentless in associating it with Jewry -- thought as quintessentially rationalist, conniving, cosmopolitan and thereby subversive. In that, it is a rare piece which takes seriously the significant intellectual pedigree of anti-Semitism which has continued influence over major schools of social thought.
However, the problem with Frim and Fluss' otherwise excellent piece is straightforward: all of this was equally true of Enlightenment thinkers. They, too, frequently justified the Enlightenment project by virtue of how it rejected the Jews and Jewish values -- who, in this tradition, were viewed as backwards, insular, tribalistic, and superstitious. Voltaire was a raging antisemite, but even friendly French emancipators unashamedly demanded the abolition of Jewish distinctiveness and the full Jewish assimilation into "neutral" French life. Marx's "Jewish Question" posited Jewishness itself as a problem to be solved, while Fichte's (a more borderline case in the "Enlightenment/anti-Enlightenment" divide) proposal for Jewish emancipation was that "their heads should be cut off in one night and replaced with others not containing a single Jewish idea."
In a world that was and is foundationally antisemitic, standing in opposition to Jews carried and carries rationalizing force. It is depressing, but actually not that surprising, that a great number of Enlightenment/Anti-Enlightenment debates took place on the terms of "who's more Jew-y?" This doesn't exculpate the antisemitic elements of the anti-Enlightenment tradition, which are and remain very real. But it is by no means the case that their Enlightenment counterparts have remained unstained. The real moral of the story here is neither pro- or anti-Enlightenment in itself, but rather lies in the cognizance of how deeply antisemitism infects the Western philosophical tradition because this philosophical dialogue to an alarmingly large extent has been about who better repudiates "Jewish" characteristics.