And how can a non religious government, an anti religious government for that matter, make a determination who is Jewish? That is the utmost of a religious decision.
Score yet another one for separation between church (synagogue) and state.
Issues like shabbas buses, Toeivah Parades , Treif food , Army issues etc will constantly come up and you have to decide how to balance the Torah and the belifes of people who disagree. Once Moshaiach comes, thats different , but he is not here and you have to govern now. Forcing torah laws will not work and likely backfire.
And what you create is a hybrid chazer sticking out its hooves. Better off not starting and not messing with Yiddishkeit to make it fit your “State” and its needs.