I posted earlier to the OP that the definition of zionism is basically the belief in a Jewish homeland in Israel. And opposition to that idea might be fine if you have an actual, cogent, alternative ideology by which you think people should live in the principles of equality.
For example: a person might argue there is no need for a specifically Jewish state, and a multicultural state should be formed for both Jewish / Muslim persons with equal rights of immigration and so on. Of course, they would need to get the Palestinians to agree to that, and find a way to deal with the fact that these two groups have completely opposed laws, ideals, value systems and so on. But nevertheless, it's a valid argument that isn't antisemitic.
So I do not believe anti Zionism is always antisemitic, although being anti Zionist is usually a result of already being antisemitic and it certainly fosters pernicious antisemitic ideals amongst the wider population, and I will explain why and how that works for anyone who is interested.
First of all, the word “Zionism,” resonates for many people as an expression of hope for Jewish survival and liberation. Zionism was conceived as a way for Jews to escape the oppression of antisemitism, in Europe, in Russia, and across the Middle East, and to live free, as other people live free. That isn't bad, is it?
Anyone who has read and knows the history (and I have posted extensively on it) knows they did not live free. Not anywhere. Not ever. But despite that being pretty reasonable and in no way related to racism or wanting to dominate others, in our day the left has turned the word “Zionism” into an anti Jewish swear word which they have constructed to mean whatever they want it to mean.
So in effect, the left defines Jews' Zionism for them, against their will, and without discussing it with them. It defines Zionism as racism and as support for apartheid. In so doing it defines most Jews against their will, as not decent human beings like the rest of humanity.
Then a few unusual Jews - religious extremists or hard left extremists - who are are willing to take on this same erroneous meaning are presented as evidence that this is entirely correct. They are then classified as “exceptional Jews” who are willing to denounce Israel and Zionism. And Jews on the wider picture are put in a position where unless they agree with this distorted definition of Zionism and denounce most of their kin, they are bad people.
It becomes a creator of antisemitism when "anti Zionism" takes on the modern left's new definition of what Zionism even means and that becomes propagated and associated with most Jews. People who are hostile to Zionism have given the word "Zionism" a meaning that reflects their own hostility rather than the actual meaning of the word to the people whom it describes. The OP, for example said she thought it meant "genocide". Tt certainly doesn't mean that to the people who are Zionists but if everyone defines them as that, then the damage is done.
Anti Zionism is common amongst the modern left because it is based on what the Marxists see as an “idealist” system of living - equality and so on. It understands Israel as the manifestation of racist ideology (that Jews have an ethno state because they think they are superior), rather than it being a result of the material reality (that the history proved that Jews were actually unable to life in this "idealistic" world without being ritually killed and subjugated).
In the leftie mind, "Zionism" must be racism because a country that is majority Jewish and that is not a state for all its citizens past and present, must be racist. It figures that the state prioritises the rights of Jews, on the basis of their ethnicity or religion, over those of non-Jewish origin must be racist and bad. They dismiss entirely that for the last 700 years (including now) that the same applies to every Muslim state on the planet. It dismisses the reality that Jews lived for 600 years as Dhimmi (which truly is apartheid) and under constant threat of death.
That blatant double standard is justified with the idea that Israel should not exist anyway, as it was founded on the settler-colonial theft of land, which rightly belongs to “indigenous” Palestinians. They don't consider the possibility that Jews are also indigenous, or that Arabs may be migrants (a lot are).
It fixates on the idea that there are many Palestinians who are now not living where there families lived 100 years ago. But Jews today do not live where their families lived 100 years ago. Their families did not choose to move but were exiled or had to run away from certain death. Most of them did not choose where to go, they went where they would be allowed to go (which was practically impossible to find). That is also dismissed as whataboutery.
The left propagates an idea of Israeli immigrants as again, terribly evil, but it ignores the fact that Jews are a tiny, tiny world minority and hence even those of European recent ancestry are often connected to Israel by family. Wanting to commune together within norms of culture is normal humanity - not racism. People's around the world do this.
Most perniciously of all, the new definition of “Zionism” in the modern left's imagination frequently characterises Jews as participating in dishonest global networks, conspiracies of lies and propaganda, in their own selfish interest. The idea of a "Israel lobby", controlling the world and policing what we say in order to allow them to continue being racist toerags without criticism. Even regular British Jews are accused each day of being part of this nefarious scheme.
So really modern "anti Zionism" often has little to do with proposing equality and multicultural ways of living together in equality. It more often that not targets solely Jews as underserving of freedom and safety from more dominant groups, and re-definitely their perfectly understandable hopes for the things all others take for granted as an expression of their negative characteristics.
So "Zionists" become a kind of evil sub set of people, and by portraying the overwhelming majority of Jews in the world as the enemies of all that is good, anti Zionism brings back to life the general idea that most Jews are "bad". The idea of most Jews as the “enemy of the people” is re-ignited. Which really was (I hoped) an ideology that I thought was stamped out after the Holocaust.
So anti Zionism in and of itself it's anti semitic. If it has a logical basis. But certainly the way the modern left goes about it is based on very antisemitic ideas and reignites a lot of most antisemitic myths and ideas history has seen. Which makes me very sad. I should not to be made to feel ashamed for being a "Zionist" because a few socialists have redefined this lovely word that is essentially based on peace and justice to mean something they have made up entirely.
And note: I am a socialist, so this has been doubly hard to endure.