Claims made by people calling themselves "Anti-Zionists" often parallel traditional Anti-Semitic claims such as control of the media. For this reason, many people object to the term anti-Zionism as a rationalization of Anti-Semitism or a euphemism for it. Zionism, in its historically conscious sense, means the political movement that sought to establish a modern nation-state in Israel. This has now been achieved and the original immediate aim of Zionism has now become a moot point. Partially because of this, the word "Zionism" is often used now, especially by Anti-Zionists, to designate any support at all for the state of Israel. Since there is a spectrum of possible meanings for the word "Zionism," there is also a spectrum of possible Anti-Zionisms. Thus, I think it makes sense to separate the word "Anti-Zionism" from the word "Anti-Semitism."
"Anti-Semitism" refers to hostility or prejudice directed at the Jewish people. We tend often to identify "anti-Zionism" with "Anti-Semitism" because the extreme forms of Anti-Zionism carry bias to the point of bigotry and clearly involve a desire to harm the interests of the state of Israel, a desire that can hardly be said to coexist with a neutral or benevolent attitude towards the Jews that live there--and indeed all Jews (since all Jews have a stake in the connection between the People of Israel and the Land of Israel).
Nevertheless, the Jewish People and the State of Israel are not identical entities. Bigotry towards one, at least theoretically, is not automatically bigotry towards the other. What is clearly needed is a recognition that Anti-Zionism is often a kind of bigotry in its own right. Even extreme anti-Zionists may take pains to avoid anti-Semitism, but that does not exonerate them, it merely means that they exemplify a different sort of bigotry. The notion, for instance, that Modern Israel is a "European" country whose residents all have European "homelands" is a bizarre distortion which in practice is paired with the intent of harming the interests of millions of Jews. Is it Anti-Semitic? This may depend on what you mean by the word "Anti-Semitism," and perhaps the best way to avoid semantic quibbles is simply to affirm that it is a bigoted belief no matter what it is labeled.
So I think that maintaining the distinction bewteen anti-Zionism and anti-Semitism may actually provide some clarity in the face of people who claim that they are being labeled "Anti-Semites" for mere criticism of Israel. The answer to such people is that they if are entertaining beliefs about Israel that no informed objective person can entertain or exhibiting an extreme tendency to single out Israel, they may not be "Anti-Semites" per se, but they are bigots all the same.
Some people have begun to use the word "Zionphobia" to refer to bigotry or excessive animosity directed towards the stare of Israel. In order to develop a more detailed understanding of Zionphobia, we might identify some typical Zionphobic claims and patterns:
Claims:
Israel controls U.S. foreign policy.
Israel's Jews all have European homelands.
Israel (or the Mossad) carried out 9/11.
The Danish cartoon controversy was a Zionist plot.
Israel was founded as a conspiracy to hinder Muslim development.
Despotism in Arab countries is a natural reaction to the threat posed by Israel and therefore Israel's fault.
All critics of Israel are branded as anti-Semites and silenced.
Israel poisoned the Palestinian water supply to harm Palestinian fertlity.
Zionists control the media.
Israel dropped poisoned balloons into Lebanon.
AIDS is an Israeli plot.
Bird Flu is an Israeli plot.
Israel is plotting to destroy the Al-Aqsa Mosque.
Israel is intrinsically non-viable economically and only survives on foreign aid.
Patterns:
Headlines in which Palestinians are "martyred" while "Zionists" die.
Use of the word "Zionist" to refer, for instance, to anyone who criticizes the Muslim Public Affairs Committee.
Avoidance of the word "Israel" in favor of "Zionist entity" (or "fake regime" in the Iranian Press)
Putting the words "Israel" or "Israeli" in scare-quotes.
Usage of terms such as "Zionazi."
Description of clashes between the IDF and the Al-Aqsa Martyrs Brigades etc. as "Zionist Aggression."
Pretending that references to the Holocaust or Holocaust images always serve pro-Zionist ends.
References to Israeli "genocide" or a "holocaust" against Palestinians.
Vague and excessive use of the word "illegal" in reference to Israel, even reference to Israel itself as "illegal."
Use of phrases such as "colonialist settler state."
Reference to Israeli "Apartheid." (Real Apartheid mandated segregated universities and water fountains, for instance, and involved miscegenation laws and pseudo-scientific theories of white racial superiority.)