Whether public schools should or shouldn't stay out of the religious arena, it's not properly a federal power to dictate that to the local schools. Do you disagree with that?
I'm not sure because it's a deeply complicated question. I don't think the federal government has any constitutional authority over education at all, but they've seized it there as well as just about everywhere else.
Can the Supreme Court hold that the teaching of religion in public schools is a violation of the First Amendment? Yes, because they did.
So I don't know how to give you a straight answer to your question. The best I can do is to say, "no, but my opinion doesn't count."