"Only one group of religious Jews believes that Israel should not exist - the Neturei Karta"
what about the lubavitchers?
The Lubavichers are among Israel's staunchest supporters.
Lubavitchers actually serve in the Israeli army and Lubavitchers have referred to the founding of the Israeli state as "the beginning of the flowering of our redemption."
The Satmars (the largest Ashkenazic Orthodox group) are more ambivalent. They do not oppose the existence of the state of Israel, but they believe that it has no right to compel Jews to do anything and that it has no right to permit the violation of Torah laws. Only the government of the Messiah can truly legislate for Jews. Satmars do not do mandatory military service, etc.
The Sephardic Orthodox groups are enthusiastic supporters of Israel, and the smaller Ashkenazic groups more or less waver between more Satmar and more Lubavitch approaches to the question.
The Neturei Karta are the only ones who openly oppose Israel and support the PLO and there are maybe 1,000 of these.
They used to claim that the Satmars agreed with them, but the Satmar rebbe publicly repudiated them and their position two years ago.