It's true that most of the people who run Hollywood are Jews, but that doesn't mean that they're Zionists who are pro-Israel. Noam Chomsky is Jewish by birth too, but tends to side with anyone who isn't on Israel's side. As for the antisemitism accusation, I think it depends how far people take it. When they take it to controlling America or the world, that's crazy conspiracy talk that probably is antisemitic.

At the same time we could say that Hollywood is controlled by Ivy Leaguers since many are grabbed from Harvard and Yale. Even more accurate would be to say that the Left-wing controls Hollywood since there is a very McCarthyite-like treatment of those who don't toe that political line (with some exceptions).