I am not Jewish. I can't meaningfully comment on issues of Jewish identity. But I found this essay by Bertell Ollman on Judaism, Zionism, and internationalism very interesting (yes, the site is heavy on Marxism, but this essay has nothing to do with that sophomoric political philosophy):
From what I've said so far, it would be easy for some to dismiss me as a self-hating Jew, but that would be a mistake. If anything, I am a self-loving Jew, but the Jew I love in me is the Diaspora Jew, the Jew that was blessed for 2,000 years by having no country to call his/her own. That this was accompanied by many cruel disadvantages is well known, but it had one crowning advantage that towered over all the rest. By being an outsider in every country and belonging to the family of outsiders throughout the world, Jews on the whole suffered less from the small-minded prejudices that disfigure all forms of nationalism. If you couldn't be a full and equal citizen of the country in which you lived, you could be a citizen of the world, or at least begin to think of yourself as such even before the concepts existed that would help to clarify what this meant. I'm not saying that this is how most Diaspora Jews actually thought, but some did—Spinoza, Marx, Freud, and Einstein being among the best known—and the opportunity as well as the inclination for others to do so came from the very rejection they all experienced in the countries in which they lived. Even the widespread treatment of Jews as somehow less than human provoked a universalist response. As children of the same God, Jews argued, when this was permitted or just quietly reflected when it wasn't, that they shared a common humanity with their oppressors and that this should take precedence over everything else. The anti-Semitic charge, then, that Jews have always and everywhere been cosmopolitan and insufficiently patriotic had at least this much truth to it.
As far as I'm concerned, the comedian, Lenny Bruce, provided the only good answer to this question when he said, "Dig, I'm Jewish. Count Basie's Jewish. Ray Charles is Jewish. Eddie Cantor is goyish... Marine Corps—heavy goyish... If you live in New York or any other big city, you're Jewish. If you live in Butte, Montana, you're going to be goyish even if you're Jewish... Kool-Aid is goyish. Evaporated milk is goyish even if Jews invented it... Pumpernickel is Jewish and, as you know, white bread is very goyish.... Negroes are all Jews... Irishmen who have rejected their religion are Jewish... Baton twirling is very goyish".