Definitions are important. but need explication. As ever, I refer to Wikipedia.
Anti-Semitism is hostility, prejudice or discrimination against Jews. The Wiki article goes on to mention numerous incidents of anti-Semitism going back to 1069, the most recent atrocity being the Holocaust, the Nazi program of systematic and motiveless murder of 6 million Jews, as well as 4 million other unpopular groups during the second world war.
Zionism is a nationalist and political movement of Jews and Jewish culture that supports the re-establishment of a Jewish homeland in the territory defined as the historic Land of Israel (roughly corresponding to Palestine, Canaan or the Holy Land).
Jews had lived in Israel in various numbers ever since the First Diaspora in biblical times, but usually under foreign control. Zionism as defined above dates to 1896, after which five waves of Jewish migration to Israel took place, the last resulting from the Holocaust. These were resented and opposed by the existing inhabitants of Palestine, and both Jewish and Arab violence in various forms continued during the British mandate (1919-1947), partition by the United Nations and Israel becoming a member of the UN in 1949.
Under these horrific circumstances it is easy to understand how many Jews have come to identify with Zionism to the point where criticism of one bleeds across to the other. In the Guardian today Chief Rabbi Ephraim Mirvis is reported as saying that Jewish students at universities were confronted with a “wall of anti-Zionism which they feel and know to be Jew hatred.” In the same article the president of the National Union of Students, Malia Bouattia, defended herself against such charges:”For me to take issue with Zionist politics is not me taking issue with being Jewish . . . it is a political argument, not one of faith.” Her position is supported by a number of Jews critical of Zionist politics.
Racism or religious bias of any kind is wrong; but we cannot conflate a state with the majority religion of its inhabitants. If a criticism of Saudi or Iranian politics is not anti-Muslim, then criticising Israeli politics is not anti-Jewish. This must surely remain the position of the Labour movement.
One complication arises from the above definition for Zionism. It is a political movement, to be sure, but involves Jewish culture. Is it possible that Zionism is more than a simple adjective for Israeli state policy and overlaps the concept of what it is to be a Jew ? If so, perhaps we should be criticising Israeli policies not Zionist ones.