I've long maintained that is perfectly possible, in concept, to be anti-Zionist without being antisemitic (under reasonable definitions of both "Zionism" and "antisemitic"). The simplest way of doing this is through a sort of principled anarchism which objects to anybody having a state. In that case, "anti-Zionism" is not really a specific identity so much as it is the application of a general principle objecting to the existence of states to a particular state that happens to be Jewish -- and the principle doesn't operate materially differently with respect to Arab, or Japanese, or Mexican states.
Concept doesn't always (or, in my estimation, even often) translate into practice of course. And it is not a form of "censorship" or "cheating" to insist that if one wants to radically oppose the manner in which most Jews believe in their collective liberation, it might actually require hard work and difficult, nuanced judgments demanding deep knowledge of and attentiveness to Jewish histories and experiences. Saying that there can be non-antisemitic anti-Zionism doesn't compel the conclusion that it should be easy to do it.
That said, if you want a sketch on what non-antisemitic anti-Zionism might look like in the wild, you could do worse than reading this post by Jewdas (a British-based Jewish anarchist organization) commenting on the aftermath of the Chicago Dyke March fiasco.
I put this post forward not because I "endorse" it. I'm not an anti-Zionist nor an anarchist, I don't find the existence of Israel to be an embarrassment (though I certainly find a decent chunk of its actions to be so), and I have my share of objections to the "New Diasporism" model they are promoting -- not the least of which is my skepticism that the model adequately accounts for patterns of antisemitism in practice.
But what I can say is that theirs is a principled position that can be argued against on the basis of principled reasons. It is not a ticket good for the Jewish ride only (that brand of anti-Zionism can jump in a lake). It takes Jewish experience and Jewish communal life seriously, and offers a serious accounting of alternatives to collective living through a state. I might not find their alternative compelling or persuasive, but that's a far tamer and more prosaic objection than I'd level at the standard-issue forms of anti-Zionism that, say, justify expelling Jewish marchers because they have a Star of David on their rainbow flag.