Anti-Semitism always seeks to ascribe the worst traits in society to the Jewish population; anti-Zionism attempts to do the same.
In the Soviet Union under Communism, the worst perceived trait to have was to be a capitalist. Anti-Semites called Jews capitalist. In Nazi Germany, the worst charges to have against a group was to dilute the Aryan bloodline. Jews were accused of diluting the bloodline. In modern society, the worst trait to have is racism. Anti-Zionism accuses Jews of being racist.
Throughout history, anti-Semitism has manifested itself as accusing the Jewish people of possessing the trait that society perceives as the "worst". This was evident in the Soviet Union and Nazi Germany. In today's tolerant and liberal society, the worst thing a person can be is racist. Anti-Zionism accuses Jews of being just that. That is why anti-Zionism is clearly anti-Semitism in its most modern format.
Anti-Zionism does not accuse all Jews of being racist. It only accuses the Israeli state of adopting racist and prejudiced policies. To assume Israel represents all Jews is incorrect. Many oppose it and explicitly denounce its policies. To automatically assume all Jews are Zionist and are politically aligned with Israel is to fall into the same trap of generalisation and stereotyping that racists and anti-Semites do.
[P1] Anti-Zionism is just a modern form of anti-Semitism.
[Rejecting P1] Anti-Zionism is not ant-Semitism because it does not make sweeping generalisations about all Jews. It is limited to criticism of Israel.