Iran is a theocracy because the mullahs make the rules
In Israel the Rabbis do not make the rules Parliament does and Parliament is fully sovereign and can decide to do what it wants. Parliament could decide tomorrow to abolish the Chief Rabbinate and while people might protest it would happen. The fact that Parliament vests some power in the religious authorities doees not make it a theocracy.
in Israel you pick your religion, and it manages such things as marriage and birth certificates for you. The religion does not have to be Judaism. I do not know how do atheists deal with this system, nor do I know what happens with interreligious mariages.
Can bluke clarify?
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Less Is More. In my book, About Face, I introduce over 50 powerful design axioms. This is one of them.