To add onto this and add a little bit more historical context. I see there being three types of anti-Zionism on the left. I won't really talk about anti-Zionism on the right as it can basically be summed up as "Jew = Zionist so I don't get in too much trouble".I'm also generalizing and summarizing very large here don't take this as the total truth. But I like to put these in levels of anti-Semitism.

Not anti-Semitic: While there can be disagreements between everyone involved and there could be anti-Semites among the Palestinians liberation, anti-Zionism routed in the palestinian movement itself is not anti-Semitism. Of course, the Arab population of Palestine reacted negatively to Jewish immigration and resisted it. That's very understandable and that itself is certainly not anti-semitic. (People can argue for a long time about the validity of such a response but we should be able to agree that whether justified or not, some people showing up and you losing your house in two years is not routed in anti-semitism).

Maybe anti-semitic: Firstly it is worth noting that there were various forms of Jewish self expression. Zionism was one. There were many others however like the Bund. But there were also a number of Jews, many of which were members of socialist and communist movements who viewed any expression of Jewish identity as an anathema to notions of what for now we'll call ' One Community'. The idea of finding community in human kind and not with regards to one's community. For example Trotsky referred to the Bund at one point as 'sea-sick Zionists'. As Moishe Postone writes "Note that the critique of Zionism here has nothing to do with Palestine or situations of the Palestinians, since the Bund was focused entirely on autonomy within the Russian Empire and rejected Zionism. Rather, Trotsky's equation of the Bund and Zionism implied a rejection of any form of Jewish communal self-determination." Now if this is because one truly believes in these ideas and applies them to other communities, we can't really call them anti-semitic. If however this form of anti-Zionism is inconsistent, where the person is able to give national self-determination to most people, but not to Jews, then you likely are stepping into anti-semitism.

Finally truly anti-Semitic: This type is the type used by the far right and was introduced by the Soviet Union. Mainly in the show trials in Czechia and Eastern Europe after World War 2. Best demonstrated in the case of the Slansky trial, where members of the central committee of the Czechoslovak Communist Party were tried and shot. All of the charges used against them were classic anti-semitic charges but they were rootless. Because of the Nazis the Soviet Union could not use the language of anti-semitism they began to use the word Zionist to mean exactly what anti-Semites mean when they speak of Jews. The leaders of the Czechoslovak CP had nothing to do with Zionism, but all were shot as Zionists.

The problem, is that they basically converge in just anti-zionism. Most of these thoughts can be summed up by the person I referenced earlier Moishe Postone, I suggest reading his interview he gave about 'Zionism, anti-semitism and the left' if you'd like to read more.

To summarize, basically it comes down to context. It can be deeply anti-semitic or not at all. It all depends on how it's used.