> Zionism is the belief that Israel has the right to exist, and that Jews have the right to live in Israel.
Zionism is about the right of Israel to exist as an explicitly Jewish nation state. Being anti-Zionist does not mean you believe Israel should cease to exist, unless you define Isreal only in terms of ethnicity and religion.
> If you are against this, your views are quite extremist and it is hard to find understanding and accommodation, particularly among fellow Jews.
That's a fairly recent development in the grand scheme of things. Prior to the formation of Israel, Zionism was frequently contrasted with Bundism. The Bundist idea was that the "Jewish nation" is inherently a nation without borders and that Jews should organize internationally wherever they are. Bundists still exist but when Israel was created a lot of Jews adopted a more Zionist stance as the existence of Israel pretty much forced their hand in the debate.
There are still many good arguments against Zionism even now that Israel exists, especially from the point of view that just because Israel wants to be a "home country" for (certain) Jews, many Jews already have a home country elsewhere and identifying Israel as their home country only plays into the hands of antisemites arguing they're "foreigners" who don't belong in the country they were born into.
In fact, many white nationalists in the West use Zionism as a talking point to support their demand for white ethnostates: if Jews can have Israel for Jews, why can't "ethnic Germans" have Germany for "ethnic Germans", etc. The arguments of course get increasingly incoherent with places like the US where pinning down an "original white ethnic identity" requires a fair bit of mythologizing.
Arguably, Israel as a "Jewish state" is a late project of 19th century European nationalism, which largely fell out of fashion after WW2 with the increasing globalization of trade and industry and the softening of national borders through common trade areas and projects like the European Union. The perceived necessity for a "Jewish home country" was accelerated by the Holocaust (and the refusal of Allied countries to take on Jewish refugees until it was too late) but the "Jewish consensus" of universal support for Zionism is more manufactured than authentic and Israel has become as divisive as it has become unifying (e.g through the disregard towards Yiddish as a Jewish language, racism towards non-white Jews, prominent individuals like Netanyahu engaging in Hitler apologism, etc) even if you don't consider issues pertaining Palestinian Arabs.
EDIT: Since most people are likely unfamiliar with the term, here's the Wikipedia article on Bundism:https://en.wikipedia.org/wiki/Bundism
Although primarily a historical movement pre-dating the formation of modern Israel, Bundist movements still exist in many countries today and tend to be especially popular with Jewish socialists (who tend to be critical of Israel which they often perceive as an imperialist and colonialist project).