Chomsky's problem was that he allowed Faurrisson to include some of his writings in his anti-semitic, Holocaust-denying book without permission sought . . . and then defended Faurrisson's rights to freedom of expression.
Is he a self-hating Jew? I doubt it, he is more like some of the Uni profs I had who enjoyed making others uncomfortable with their self-criticism while keeping a sharp eye out for real anti-semites and Jews with their paranoia-infused view of the world.
At the University of New South Wales I had a German-Jewish professor who loved this shit. He and my father were friends and he enjoyed the huge number of grants and books donated by the government to the German and Central European Studies Depts. and Jewish and Holocaust studies at Sydney Uni through my father.
Of course I was enrolled in his classes and most were for adult learners - most of them Jewish for his courses. My father thought it would be both trial by fire for me as well as a good laugh for him to think of me being uncomfortable . . . and for the Prof (who also worked with the Simon Wiesenthal Centre for Australia and had me intern there for a summer) it was a chance to show a young German how old Jews who had suffered at the hands of the Nazis felt about the issue now and how Germans of my generation were informed and how we felt about that part of our history . . . it all ended up being quite cathartic for the wrinklies and interesting for me.
Chomsky a self-hating anti-semite? Nah . . . an agent provocateur? Absolutely