A reader, sympathetic to Israel but troubled by its existence as "Jewish state," asks: "Can you point me to any case in any example where you would say '[Country A] has the right to exist as a [Race B] OR [Religion C] state?' I can think of numerous claims like this by societies in the past, which are now widely condemned."
Actually, many, many countries, have an official religion, including not only "backwards" countries such as Iran and Saudi Arabia, that enforce religious law, but "progressive," liberal bastions such as Norway, Denmark, and Iceland (all Lutheran). By contrast, Judaism is not the official religion of Israel. Jewish holidays are government holidays, but that's like Christmas in the U.S. [Family law is controlled by religious bodies, but that's true for Moslems, Christians, et. al, as well as Jews, and is an artifact of Ottoman and British rule. My understanding is that most Jews in Israel are against the religious monopoly on family law, but it survives because the religious parties have disproportionate power. The Arab community, which is far more traditional in its religious practices than is the Jewish community, almost certainly is more supportive of this arrangement than the Jews are, so this has really nothing to do with Israel being a "Jewish state," as such.]
As for the question of "race," the problem can't be "self-determination" of a group, because the propriety of that principle seems rather well-accepted. "Jewishness" is not a racial identity, but complaints about Israel being a "Jewish state" are often put in terms of the Law of Return being "racist." The Law of Return is based on ethnic (not racial) heritage grants anyone with a Jewish grandparent automatic citizenship (the Israeli Supreme Court has held that one is not eligible for the Law of Return if one has adopted the Christian religion, because in the complex area of Jewish identity, Jews who become Christians have left the Jewish people). Non-Jewish immigrants with no ethnic Jewish background can become citizens, with some difficulty, as can, automatically, non-Jewish immigrants closely related to Jews (e.g., spouses), many of whom have recently arrived from the former Soviet Union. Arabs who lived in Israel during the War of Independence (and thus presumptively accepted the existence of Israel and were not engaged in warfare against Israel) and their descendants have full citizenship rights, but they are relieved of one of the major obligations of Israeli citizenship, military or other national service (I think this is a big mistake, but that is a topic for a separate post).
One's liberal, progressive, or libertarian hackles can easily be raised at Israel's citizenship policies. Why should ethnic background entitle one to citizenship? On the other hand, Israel's defenders would argue that given that the Jews have been the subject of massive state and private violence over the last few centuries, including one attempted genocide (by Hitler) and another one that was averted only by Stalin's timely death, Jews need a homeland/refuge where they can go with automatic citizenship rights.
Whatever side you take on that debate, the more interesting question is why the question of basing citizenship (in part) of ethnic descent only calls the right of Israel to exist into question.
My correspondent was unaware of any other countries that have an overt ethnic identity, but, judging by immigration laws, there are quite a few, and with a few exceptions (Armenia and Germany), their discriminatory immigration policies exist, unlike Israel's, without any justification resulting from persecution of that group.
For example, according to Wikipedia: "Japanese citizenship is conferred jus sanguinis, and monolingual Japanese-speaking minorities often reside in Japan for generations under permanent residency status without acquiring citizenship in their country of birth." Why does Japan have the right to exist as a Japanese state? Has this question ever been asked?
Ireland: "If you are of the third or subsequent generation born abroad to an Irish citizen (in other words, one of your grandparents is an Irish citizen but none of your parents was born in Ireland), you may be entitled to become an Irish citizen" [if, as I understand it, you register properly]. Does Ireland have the right to exist as an Irish state?
Several other countries recognize a "right of return" similar, but often broader, than Israel's (via Wikipedia):
Armenia: "Individuals of Armenian origin shall acquire citizenship of the Republic of Armenia through a simplified procedure."
Bulgaria: "Any person ... whose descent from a Bulgarian citizen has been established by way of a court ruling shall be a Bulgarian citizen by origin."
Finland: "The Finnish Aliens Act provides for persons who are of Finnish origin to receive permanent residence. This generally means Karelians and Ingrian Finns from the former Soviet Union, but United States, Canadian or Swedish nationals with Finnish ancestry can also apply."
Germany: "German law allows persons of German descent living in Eastern Europe to return to Germany and acquire German citizenship." My understanding is that this German descent may go back many generations. [Note that until recently, Germany's citizenship law was less liberal than Israel's, in that it did not allow non-ethnic Germans, including Turkish who had lived in Germany for generations, to be become citizens.]
Greece: "'Foreign persons of Greek origin', who neither live in Greece nor hold Greek citizenship nor were necessarily born there, may become Greek citizens by enlisting in Greece's military forces."
Wikipedia provides a several other examples, none of which seem to ever raise the same questions about the legitimacy of the states involved as the Law of Return does for Israel.
Of course, Israel has the added burden that the Palestinians claiming that they are the true "owners" of the relevant land, or that at least the Palestinians who fled in 1948 and their descendants should have their own "right to return". But I think that issue exists quite apart from whether Israel's Law of Return is objectionable, and, indeed, must, given that the Palestinian side is calling for even fourth generation descendants of residents of what is now Israel, who never set foot there, to be allowed based on their ancestry to return.
In short, the perception my correspondent had, which in my experience is shared by many, that Israel is a uniquely "religous state" is not only wrong, it's backwards--Israel has less of an explicit religious identity than many countries (complicated, I admit, by the fact that one can in an odd way assume a Jewish ethnic identity by converting religiously.) And Israel is hardly unique in basing immigration and citizenship policy at least partly on ethnic heritage (the thought that Israel is unique in this regard seems bound up with the confused notion that it must have something to do with Jews thinking they are God's "Chosen People," misconceptions about which I addressed a while ago here). The big difference is that unlike, say, Japan, Israel actually has especially strong, though I wouldn't say completely unassailable, reasons for doing so.
UPDATED: I meant to save this for further editing, but I accidentally posted it instead. Now that it's out there, I'll leave it up, but I don't have time to moderate comments now. I'll open comments anyway, but ask commenters to be especially careful to keep their comments polite and on-topic.