It’s more akin to a theonomy really, since Israel is designed upon the Word rather than a specific religious institution.
Not exactly, because the State of Israel violates the Jewish religion all the time, and many non-Jews are citizens with full rights, including 20% Muslims. You can’t separate state and religion in Israel, just like you can’t go to a marriage counselor and talk about everything except sex. It’s a big part of the picture, and to pretend it is not is to be in denial. But it’s not the whole picture, either, anymore than sex is all that there is to a marriage.