There clearly are people who claim Israel (and Jews in general) as a shared identity and cultural group have no right to exist. These people are traditionally called Nazis.

Yup, and those Nazis largely supported the Zionist mission of a Jewish state, both because they wanted the Jews to emigrate out of Europe and because they hated Arabs almost as much as they hated Jews. Nazis and Zionists share a strictly defined understanding of cultural and ethnic boundaries, and a belief that geographical boundaries are a reflection of those boundaries (or ought to). It's only really tricky if your understanding of Zionism and Israel is limited to the specific group that is doing the cleansing.

The Israelis aren’t simply a group of Ashkenazi Jews who moved to the Middle East during the Holocaust. They’re a people who have lived in the area for thousands of years and maintained a distinct culture throughout occupation by other empires.

The jewish diaspora is almost as defined by their shared cultural heritage with their middle eastern neighbors as it is by their origin. You can't draw a clean ethnic or cultural boundary around Israel that's separate from their arabic brothers and sisters. That's exactly the problem with zionism - it attempts to forcefully separate the cultural inheritance of its arabic history and expel it from both the geographical and cultural boundaries of Israel.

People who oppose Israel as a Jewish state do so because they see Zionism as a mission of ethnic and cultural purification, not because it's a symbolic representation of Jews as an entire people. That's what makes the conflation of anti-zionism and antisemitism so nefarious.