The King James Bible is such a gargantuan influence on English prose that it has to be taught as Literature in an English class which shouldn't address veracity one way or the other. The rest is up to religious instruction at home.
The notion that religion is "private" is based on the enlightenment idea that all religion is subjective rather than objective, and is the product of philosophical speculation rather than objective Divine Revelation. In ancient Israel you may be sure there was absolutely no separation of religion from the state, nor will there be in the Messianic future.
It's one thing to teach the KJV for its language, quite another to teach the "documentary hypothesis" or to tell the captive audience that it's all bunk.