I am going to argue something different, and I would like you to seriously entertain the idea. The argument is: anti-Semitic harassment and anti-Zionism are part-and-parcel.
Consider: imagine for the sake of argument a universe that is exactly like ours, except in that universe, Israel is prosecuting the war in Gaza reasonably well, as perfectly as it is possible to prosecute any war. They actually do minimize civilian deaths, not commit any war crimes or genocide, ensure that aid gets where it needs to go. They simply want to get rid of Hamas. In that universe, the war is actually a measured and rational response to the Hamas provocations of that universe, October 7th actually happened, etc.
Please answer honestly: in that universe, how do you think the world responds? Does Hamas still claim genocide? Does the "Gazan Ministry of Health" still issue a daily death toll that is strangely absent of combatants? Does the BBC and al-Jazeera, et. al. still quote those statistics with neither qualification nor caveat? Does South Africa still take Israel to ICJ? Does the UN security council still issue resolutions against Israel without reference to Hamas or the hostages?
I believe that the answer to those questions would be identical to this universe. Would you agree? If not, what is the mechanism by which the world could tell the difference? What trustworthy organization would impartially inform us all that there is no genocide in a way that you yourself would believe it?
I believe most anti-Zionists would behave quite the same in that universe, because for them, Israel's existence is a problem, and the accusation of genocide is a tool in its dismantling.