The suspension of British MP Ken Livingstone for the (inaccurate) comment that Hitler was a Zionist has raised charges of anti-Semitism within Britain's Labour party. These charges are part of a larger debate over whether being anti-Zionist is anti-Semitic. Given a Western norm against anti-Semitism, some fear that anti-Zionism is merely a dog whistle for more notorious prejudices. Others point out that Zionism as an ideology is independent from Judaism as a religion and criticism should be fair game.
The intractability of this debate shows that the question of whether anti-Zionism is anti-Semitism is far too broad to be useful. It risks getting bogged down in semantic debates while ignoring the more important question of how to build discussions of Zionism that are open enough to include dissenters, but regulated enough that bigotry and prejudice don't silence supporters.
In addition, neither Judaism nor Zionism are easily defined. Both are professed by large, pluralistic, longstanding, international communities. Both are characterized by internal debates around a core set of principles. This means that blanket statements about all anti-Zionism or all anti-Semitism do a disservice to both. A better approach is to specify which types of anti-Zionism are and are not anti-Semitic.
As with racism, sexism, homophobia, and able-ism, anti-Semitism can be unconscious. Good specification can be useful for bringing these unconscious biases to the surface. That being said, an anti-Zionist but not anti-Semitic argument has:
1) Well-specified terms. It does not talk broadly about the nature of all Zionists. Rather, it acknowledges - explicitly or implicitly - variation that has existed among Zionist movements since at least the First Zionist Conference in 1897. In addition to variation across movements, individual Zionists held complex views as well. Albert Einstein supported a bi-national state in Mandate Palestine, but also campaigned for the World Zionist Organization and was a strong supporter of Hebrew University.
Anti-Zionism without anti-Semitism also acknowledges changes in these movements over time. As Nadav Shelef points out, for example, Revisionist Zionists originally considered present-day Jordan as the "Jewish Homeland." Today, few members of revisionism's progeny - the Likud Party - would argue that Israel should annex Jordan. Zionism, like most political ideologies, comes in many flavors and changes over time. A purely anti-Zionist argument acknowledges this variation by specifying which kind of Zionism and which time period it is addressing.
2) Generalizable principles. This means that the tenets of the argument are based in principles that apply beyond Zionism. Take the idea that Israel should not exist because Judaism is not a nation. This idea is a purely anti-Zionist and not anti-Semitic if the criteria of "nation" applied to Jews are reasonable and widely applicable to other groups. It is not anti-Semitic to say that the Jewish nation does not inherently deserve a state only if one also believes Kurds, Armenians, Roma, and other historically persecuted minority nations do not inherently deserve a state either. The values of an anti-Zionist argument that is not anti-Semitic should be broad-based and applicable to other cases.
The difficulty for generalizability, of course, is that Israel is unique in many ways beyond its Jewish character. It is a non-Muslim state in the Middle East, the only state whose leadership includes those of European descent, and the largest recipient of US foreign aid. The Jewish people are also unique in that analyses understand them simultaneously as a religion, ethnicity, nation, and culture. Criticism of Zionism that bases its argument on these unique aspects of Israeli or Jewish character is not necessarily anti-Zionist. That being said, some of these factors interact with Israel's Jewish character and purely anti-Zionist arguments should acknowledge this interaction. US aid to Israel may be affected, for example, by American religious views towards a Jewish presence in biblical Israel.
One final observation: Specific terms and generalizable principles are not only good argumentation but respectful as well. They acknowledge the pain of those who identify as Jewish and/or Zionist, a pain which is real and to which they are entitled. As with anti-Palestinian nationalist arguments, one can be reasonably anti-Zionist without being disrespectful, rude, and obnoxious. One doesn't have to be polite to avoid being anti-Semitic, but it bolsters confidence that the claim is about an ideological point, and not thinly-veiled prejudice against Jews or their historic homeland.
In other words, make your case but don't be a nudnik.