It wouldn't likely be constitutional in the US. Some of the Founding Fathers were vehemently against religion being taught in schools and their policies are reflected in law. Among them, Thomas Jefferson was the most stern in his disapproval of the practice. He considered religion a strictly and profoundly personal matter and thought that when institutions tampered with it or forced it on the people, it compromised their religious liberties.
Anyway, even if you made an effort to develop an unbiased understanding of each religion in policy, you know that the system would be abused by those who favored one or the other. I learned about Judaism, Islam, Buddhism, and Hinduism in Catholic School. They were mere scraps and usually only taught in the context of "and this is why we're right." There's no reason to think that pre-dominantly Christian public schools will be any different. I mean, look at how they treat religion in history. You can always tell what religious background the teacher/writer comes from.
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I have not the kind affections of a pigeon. - Ralph Waldo Emerson