The State of Israel is both Jewish and democratic. The Jewish dimension of the state is given voice through the support of Torah culture. But not necessarily through Torah culture of a single stripe. The culture of Torah consists of infinite coloration. The state is required to help all shades find expression not only because of the principle of parity but also because of the nature of pluralism.
Pluralism is an aspect of democracy and Israel is a Jewish state which is also democratic.
What this unprecedented formulation calls for is not a separation of state and synagogue, but parity for all religious groups. This was the political arrangement in major Jewish communities throughout central Europe, like Berlin, Frankfurt and Vienna, before the war. Despite the religious fragmentation that came with emancipation, the local community maintained its unified structure by funding equitably the religious institutions of all movements. And this is the principle adopted by local federations in North America, the wholly voluntary equivalent of European communities once mandated by government legislation, as they increasingly aid the schools and synagogues of the religious sector of Jewish life in their domain. I have never deemed separation feasible for Israel.