I think if you do what the other people here are telling you to do, you will not get this guy in trouble, he'll get YOU in trouble. I am not disputing that he's a total asshole. I am simply stating the unfortunate fact that people like him are in firm control of academia right now, and going against such people's prevailing orthodoxy can get you in very deep shit.

I don't want to give a long speech, but I am pretty in tune with what's going on on campus right now. Notice how when you tried to correct your professor, the whole class sided with HIM, not you. To laugh at such a "charming joke" is to side with him.

To the far-right, the Jewish person is actually less white than a black person. That is because in the drivel of Aryan race theory, the Jewish person is at the very bottom.

To the far-left, the Jewish person is white. Especially if you're a male, you're a white male, so again at the very bottom. The Jews, to the far-left are not victims of persecution, they're wealthy white people and enemies of the Muslims, who are deemed an oppressed minority though they are not oppressed and are not a minority. Far-left congresswomen Ilhan Omar and Rashida Tleib constantly say anti-semitic things, Pelosi couldn't even muster a condemnation of anti-semitism and they keep saying such things.

College right now is disproportionately controlled by the neo-Marxists. That is, far-left blacks, far-left LGBT and far-left women/feminists. If you so much as disagree with them properly, they will seek to silence you, and if you try to get them in trouble, you might end up BLACKLISTED and unable to find employment after graduating from your I-assume-expensive college.

So, if you go to the college faculty and staff and report him, you might be smeared as a racist and a lot of bad things might happen to you.

Keeping in mind that current academia is like this and there is no longer any true free speech on campus, simply accept that people like this professor are pond scum, keep your feelings to yourself, graduate, get a good job, and get your revenge on them by having a good life while they simmer and boil in their own festering hatred.