"So, rather than demand that Palestinians recognise Israel as a "Jewish State" as such - adding "beyond chutzpah" to insult and injury - we offer the suggestion that Israeli leaders ask instead that Palestinians recognise Israel (proper) as a civil, democratic, and pluralistic state whose official religion is Judaism, and whose majority is Jewish. Many states (including Israel's neighbours Jordan and Egypt, and countries such as Greece) have their official religion as Christianity or Islam (but grant equal civil rights to all citizens) and there is no reason why Israeli Jews should not want the religion of their state to be officially Jewish. This is a reasonable demand, and it may allay the fears of Jewish Israelis about becoming a minority in Israel, and at the same time not arouse fears among Palestinians and Arabs about being ethnically cleansed in Palestine. Demanding the recognition of Israel's official religion as Judaism, rather than the recognition of Israel as a "Jewish State", would also mean Israel continuing to be a democracy."
If it looks like a Jewish State, walks like a Jewish state, and quacks like a Jewish State, it's probably a Jewish state.
What's the difference between recognizing Judaism as the official religion of Israel and recognizing its Jewish character? What Nusseibeh describes here is what most Jewish Israelis mean and want when they say that Israel is the Jewish State - a democracy with a Jewish majority and Judaism as the official state religion.
I'm fine with Palestinians recognizing Israel's Jewishness without actually saying the words "Jewish State". I'd even settle for less, with Palestinians just agreeing that their new state would not work against this internal Israeli matter militarily, diplomatically or otherwise.
Update (October 7): More on Nusseibeh's article here.