First off, I am an anarcho-capitalist, and therefore do not acknowledge the right of any state to exist. That said, this is a valid question that even an-caps must weigh in on, as we must engage society on terms they accept in order to be productive. Our (sometimes pseudo-) intellectual bloviations are of very little practical use, as clearly evinced by the majority of posts so far in this thread.
To the extent that in the creation of the Jewish state the rights of Palestinians have been violated, the Israeli Jews, as willing participants (no population that I know of can be said to be more amenable to description as members of legitimate social contract than Israeli Jews), have given up their rights in proportion to their assault on the legitimate property rights of Palestinian Arabs. Through proportionality, one can determine that the Israeli Jews have therefore not only ceded a just right to any property made theirs via the 1947 agreements overseen by the U.N. (again, assuming for argument’s sake the legitimacy of such agreements), but to all property owned via just acquisition by Jews living in Palestine prior to the Balfour Declaration.
To take it a step further, one can show how, under any semi-libertarian legal ethic, the UK’s grant of property to Israeli Jews is null and void. Kings are the property owners of their entire kingdom, and likewise governments often own property in this way. This is property, but it is not justly owned property, as the government did not homestead it or acquire it justly from its original homesteader. This property, therefore, is rightfully owned by (the just property of) either those it was stolen from, or if they or their heirs cannot be found, the first user.
The United Kingdom owned Palestine, and ceded it (albeit under violent coercion from Jewish terrorists) to the state we now call Israel, which now gives land grants based on the religious heritage of individuals who wish to move to the territory. There was no legitimate transfer of just property, as the property was not justly owned. Original owners could not be traced, as the United Kingdom got the land from the Ottoman Empire. Therefore the property continued to be justly owned by those occupying it, the vast majority of whom were Palestinian Arabs.
Regardless of the continued unjust aggression shown both by the IDF in, well, most of their dealings, and by those perpetrating what the Israeli government persists in calling “settlements” (forced annexation), the current Jewish occupiers of Palestine have no right whatsoever to more than 3/4 of the land they occupy in the same way that the recipient of a gift of stolen goods has no right to those goods in the face of the rightful/original owner of those goods.
So, no. Israel has no right to exist, even in comparison with other modern states. This is not a libertarian judgment, and it is certainly not an an-cap judgement. It is a judgment based on any legal conception that does not include the phrase “might makes right” as a central tenet.