When the settlers first arrived in New England, they formed an alliance with the Wampanoag Indians which protected them from other Indian nations of the region and helped them adapt to the territory. In exchange, the settlers agreed to allow the Wampanoag to maintain their traditional religious ways. This agreement held for the first generation of settlers. The children of these settlers reneged on this agreement and started to move the Wampanoag into "praying villages" in order to teach them a proper Christian lifestyle and obliterate the Wampanoag way of life. The Wampanoag responded with what became known as "King Philip's War," which the settlers won and subsequently exterminated much of the Wampanoag community, comparable to what happened to some Jewish communities in Europe during World War II.
Centuries afterward, the United States started settling the southwest territory, including the Apache homeland. While many Apache resigned themselves to accept foreign control of their land, one notable resister was Geronimo. Eventually, federal forces captured Geronimo, ending the Apache resistance against US control of the native land. During the centuries between King Philip's War and conquering the Apache, America had advanced civilizationally such that Geronimo did not suffer King Philip's fate, that of having his head placed on a pike. Instead, Geronimo was merely brought east of the Mississippi where he subsequently became an honored guest at events like Teddy Roosevelt's inaugural and at the St. Louis World's Fair. However, for all the honors Geronimo received in the East, he was never allowed to travel west of Missouri.
With this background, one can now discuss the relationship between anti-Zionism and anti-semitism. Someone can be an anti-Zionist without believing that what was done to the Wampanoag should be done to the Jews. There are those who believe that that should happen, for instance, there was an event where David Horowitz spoke and a woman from the Muslim Students Association challenged him during question and answer. In response, Horowitz asked if she supports or opposes Hezbollah's statement that they welcome the Jews moving to Israel so as to make it easier to eliminate all of international Jewry in one shot, to which she expressed support. However, that is not an essential element of opposing Zionism. One can oppose Zionism and support Jews receiving all the honors that Geronimo received, provided that they receive those honors, as Geronimo did, far away from their homeland. If you hold no amount of honors bestowed on Geronimo justly compensates him for being torn from his homeland, then you must admit that no honors bestowed on Jews in the diaspora removes the stain of anti-semitism from denying the Jews their homeland.
Update: It was David Horowitz, not Richard Landes as initally reported, who exposed the hater from MSA. I have also added a link to the video and specified the organization of Horowitz's challenger.