A large part of it is because he is ethnically a Jew, yet he is not a Zionist. He is quite critical of many of the policies of the Israeli government and the mistreatment of Palestinians. For that he is often even labeled as an anti-Semite, as many others are, which is beyond absurd. It just shows to what depths some are willing to go to try to discredit others for merely disagreeing with their own views.
And as far as being
"anti-American" is concerned, for many of those who claim he must be that as well:
He's right about the similarity between "anti-American" and more nasty things. But he doesn't see it as natural tribal fighting - he'd probably blame it on some massive capitalist propaganda machinery. That is, some transcendental force corrupted man. Following on that, he doesn't see the difference between America and Germany, because that transcendental force still exists in some form. Yet in America he is in fact fairly well protected despite the transcendental force, and the "anti-American" lynching mob can't really do much to him.
To put it another way, bad things like imperialism is very much contained in America, compared to what 19th century colonial empires were like. It's still pretty bad, of course, and efforts to restrain it further is commendable. But that doesn't mean we were not on the right path. That doesn't mean there has been no progress - progress he could not see because he inherited the faulty logic from Marx where everything is categorised as either good or bad, where any bad stuff must be abolished. In the real world "things are still pretty bad" doesn't mean "things are as bad as before". Exaggerating America's ills to the level of "[w]e are just like the Nazis" is neither scholarly nor respectable.
In particular, "things are still pretty bad" doesn't mean we should give up on everything we've been doing, and start over in some unspecified way. In this Chomsky is like what Marx was. Their contribution to the society was limited to raising the awareness of social ills, which was very admirable. But they offered no solution other than a very rough sketch of heaven. I think Chomsky will freely admit that he has no actual plan or design for an ideal, but workable government. This is fine when nobody seriously listen to him. But if people take his revolutionary-ish views seriously, and begin overthrowing the existing order before having a concrete idea of a plausible alternative, what you'll end up with is another Comrade Ulyanov, regardless of how "tyrannical" the existing order is. By contrasting the actual world with an ideal paradise, they created an irresponsible promise which historically has been abused in unspeakable ways. For that they are guilty, with Marx more (innocently) so, as he actively fought to realise it for many decades. Chomsky had a much smaller impact.
And I'm not convinced about "[a] large part of it is because he is ethnically a Jew". That sounds rather like "Chomsky is anti-American". A lot of people probably hate him simply because they don't like his fierce criticism.