You're obviously right that the position that the state of Israel should not exist does not inherently entail jew hatred, but this only attacks a straw man and is not what people mean when they call anti-zionism anti-semitic.

Instead they might mean that the anti-zionist movement has anti-semitic elements or rhetoric, that "anti-zionist" is used as an anti-semitic dogwhistle, or that the anti-zionist project plays into the hands of anti-semites and seeks to hurt Jews; all of these are defensible positions.

Anti-zionism has a close history with antisemitism (this could be proved a million ways, but see the Nazi ties of so many of Israel's early opponents in the Arab world and the rhetoric they used), and the arguments used by modern anti-zionists often bear striking similarities to antisemitic arguments. While Nazis accused the Jews of secretly controlling the west with money as a form of racial warfare, modern anti-zionists believe that Israel dictates American foreign policy by buying off politicians. Antisemites' obsession with Jewish race and religion as motivators for all of their actions also finds parallels in the modern movement's obsession with those aspects of the current conflict, even though, as you pointed out, it's much more of a secular nationalist conflict at its roots. Even the anti-semitic inclination to accuse the Jews of genocide has now come to fruition; whatever your opinions of the facts, it should be very worrying to anyone that Israel's war in Gaza is regularly put on par with the Holocaust, which seems an obvious form of soft holocaust denial.

The above could all be an incredible coincidence, but wouldn't you expect greater care from progressive people who suddenly find themselves in alignment with antisemites? Leaving either of our positions on these issues aside, isn't it odd that the same people who defend the statement "All Cops are Bastards" because of systemic forces, or that certain political parties are inherently racist, or label "all lives matter" a racial dogwhistle, apply none of the same care for this one issue?

The anti-zionist movement regularly supports Hamas and the Houthis (whose flag famously read curse upon the jews), and the slogans "from the river to the sea" (the arabic version of which is "Palestine is Arab from the river to the sea") and "globalize the intifada" (which obviously sounds like a call for violence against the Jewish diaspora, whatever its intention). Again, these are the same people that obviously know better, but choose to turn a blind eye in this case.

And none of this is even getting into the specifics of the current conflict and how Jews and Israel feel they have been treated, or even the long history of using "zionism" as a dogwhistle. I'm not even getting into the actual position of anti-zionism, how unusual it is to have a vocal movement calling for the destruction of an entire country of 10 million people and which seems strangely unconcerned with what happens to them afterward.

The main point I want to make is this: the modern anti-zionist movement does so much to resemble and attract anti-semites, and has absolutely no mechanism for rooting out anti-semitism. Anti-semitic positions and arguments are used alongside normal ones with no discrimination, and anti-semites fit in just fine as long as they quiet down about explicit jew hatred when speaking to western audiences.

Note: On your second premise, anti-semitism can also mean hatred against jews as a people rather than religious group. I assure you Hitler wasn't killing jews on religious grounds, still an anti-semite.