An Islamic state is a theocracy which uses Sharia law as its basis for government, laws, and social norms. Both Iran and Saudi Arabia are Islamic states.
Israel is not a Jewish state because it is not a theocracy that bases its government on Jewish law. Instead, Israel is a Jewish homeland because it is a Jewish majority state which offers refuge to all Jews fleeing persecution elsewhere. In addition, Israel welcomes the immigration of Jews living in the Diaspora who choose to live in the Jewish homeland. Requests for immigration from other people are evaluated on an individual basis. Israel is a democracy which has complete freedom of religion. The royal family of Jordan has custodianship of Muslim and Christian holy sites in Jerusalem. Over 20 percent of Israeli citizens are Palestinian Arabs.
Since Israel is a Jewish homeland, Israel can accept the refusal of President Mahmoud Abbas of the Palestinian Authority to recognize Israel as a Jewish state. Israel can reciprocate by refusing to recognize a future Palestine as an Arab state.