One interpretation of "Zionism" could mean the idea that Israel should be an ethnically and religiously Jewish state that comprises the Biblical land of Israel, and that everyone else should be second-class citizens; and so simply saying that Israel should be a democracy that gives equal rights to all the people living within its borders, or that Israel should respect the Palestinian territories, would be "Anti-Zionist". Under this interpretation, "Anti-Zionism questions Israel's existence" really means "Anti-Zionism questions the existence of one particular vision for what Israel should be". That's not really a bad thing.
If, on the other hand, "Anti-Zionist" means the abolishing the Israeli government and re-partitioning the territory back into its pre-1948 states -- I mean, yeah, that's pretty bad; but I've never heard any of my left-leaning friends advocate anything like that, and such a desire would be really incompatible with everything else they're in favor of.
But these are just guesses, since you didn't provide much context.
Having said that, in my experience, a lot of people have some vague sense of "Israel should not be a purely Jewish state, should allow equal status to everyone else, should give the right of return to all Palestinians [implicitly meaning that it would no longer be a Jewish majority state]" etc.
And most people don't have a good answer to the question: Poland is a state for ethnic Polish people, Spain is a place for Spanish people, Japan is a place for Japanese people; why can't there be a country that's for Jewish place? Why is a country for Jewish people somehow illegitimate?
(There are good answers given the history why this particular instantiation of Israel is a problem. So good that nobody has been able to solve these problems for so many years. But many people talking about this don't know those reasons - they just vaguely think "Israel bad, not allowing anyone equal rights is 'apartheid'" etc.)
I think the point is that those countries you say are "nation states" are in fact turning away from being nation states, or already have. Most of Europe learned from the 19th and 20th centuries that nationalism (despite being very romantic in many ways) ends in disaster. I am from the UK and it cannot be said to be a nation state, if it ever was. My country is full of people with immigrant backgrounds from all over the world with full citizenship rights who are a million miles from being "ethnically English" or "ethnically Scottish". As it should be.
So yeah in my opinion, an "English nation state" is undesirable. I don't want it. I'm glad we're not one.
Give us a few, I'm interested.
Zionism at its core is the belief that the Jewish people have the right to self-determination in their ancestral homeland. This is precisely what "anti-Zionism" opposes. Middle Eastern/Arab "anti-Zionists" advocate for exactly what you mentioned in your second paragraph. Additionally, depending on their political affiliation, some may seek the subjugation, expulsion, or harm of the Jewish population in Israel/Palestine. The percentage of Palestinians advocating for a one-state solution with equal rights for all is at most 33%, according to the Palestinian Center for Policy and Survey Research (PSR).
Your "left-leaning" friends may not have expressed anything like that and might simply want to express solidarity with the perceived "weaker" side. However, by proclaiming to be "anti-Zionist," they are undoubtedly associating themselves with some aspects of hardcore Palestinian nationalism. It's puzzling to me how this is compatible with traditional left-leaning stances and why any self-described left-leaning person would want to be associated with that, except due to extreme ignorance about the meaning of the words and the actual situation on the ground.
