Anti-Zionism does not seek to deny Jews the right to self-determination. It merely disputes the right of the state of Israel to exercise that self-determination at the expense of the Palestinian community. Anti-Zionism, in the purest definition of the term, is the objection to Israeli expansionism and the suppression of the Palestinian people. There is nothing anti-Semitic about it. Nor does it deny Israel's right to exist. It is simply the promotion of equality and Palestinian rights.
Even if anti-Zionists did question Israel's right to existence, it wouldn't be anti-Semitic. Not all ethnicities and religions have the automatic right to a nation-state. The Kurds, Scots, Catalans, Kashmiris, Tibetans, Lombards and Uyghurs do not have a state. They have a right to exist in a pluralistic and tolerant society. But they do not have the right to demand the formation of a nation state.