With the risk of splitting the hairs even more, I think that what is commonly meant by "the right of the Israel state to exist" is that the Jewish people have a right to govern themselves as a sovereign nation in the land of Israel.
That the Jewish people have a right to govern themselves as a sovereign nation in the land of Israel.
And it's perfectly possible to question this claim (it is not ipso facto a "right") without being even in the least antisemitic, or wishing physical harm on anyone. Being as you're leaving out the fact that this "sovereign nation" was carved out of another people's land, fundamentally denying their right to self-determination.
It is this usurpation and denial of the rights of the indigenous inhabitants that people question, when they express doubts about the supposedly inalienable "right" of the State of Israel to exist.
(And yes - this generalizes to all countries; it's perfectly reasonable to question the "right" of any country to exist, or to exist with its currently claimed borders).
The reason why I left out anything was to avoid my clarification being taken as evidence of some personal bias. Alas I failed.
As you seem to agree that most modern nations have been borne out of injustices of some form or other, I feel obliged to ask this: isn't it taxing to deny every country's right to exist? It feels like it would be if you want to live in a moderate society where people want bygones to be bygones, especially the kinds that nobody can do anything meaningful about.
Personally I feel like the more productive way of arguing is for diminishing the injustices that are happening right now, not against the reasons why those injustices happen in the first place.
Isn't it taxing to deny every country's right to exist?
I don't see this stance so much as denying the rights of these countries to exist.
But rather, as recognizing that all of them are, for the most part -- faits accomplis. And in particular -- that we are free to disregard obligations imposed by others to pretend (with them) that they have (and at this point I am no longer using your words, but generalizing) some inalienable, "God-given" right to occupy a given piece of territory, within whatever borders they choose to proclaim -- and at the expense of the rights of those already living there.
So on balance, I see this is a decidedly less taxing stance to take.
At the same time -- I'm very much in the "bygones be bygones" camp, as applies to the vast majority of cases. Which doesn't mean, however, that aren't certain major territorial disputes around the world that aren't yet quite ready for the "bygones" designation -- and in fact still need to be properly adjudicated (or barring that, at least protected from deteriorating / being encroached upon even further).
The situation in the West Bank, Gaza, East Jerusalem and the Golan Heights being one of them.
