It seems to me that for safety’s sake, we ought not allow any taxpayer-funded religious education regardless of the source. While congress may not create the curriculum, its existence in public schools would construe government approval.
It might be construed so ignorantly. There is indeed that mental virus: that whatever happens publicly happens by government approval. This attitude cannot be eradicated by education reform, which pursues a much simpler goal of replacing the useless system that we have with an education that is available regardless of income, is controlled in essential part by the parents who are primary educators, and is in full accordance with the Constitution. There is absolutely no legal or logical reason why school kids can play football, or baseball, or run track, or play drums, but they cannot learn what is truly necessary for their future lives: how to be good, moral and knowledgeable Catholics, Lutherans, Jews or Atheists.