That's the best argument yet against public education... education must be based on some fundamental conception of the world, which is by its very nature religious. So if the state cannot make an establishment of religion, it similarly is not permitted to make an establishment of education.
Even if what you assert is true (I do not think it is, but in any event the matter cannot be decided unless we agree on what 'religious' means), you would still have the quarrel over which religion to use.
There are some rather awkward places that have adopted exactly this approach--look at the madrassas of Pakistan.
The only difference between your point here and the program adopted by the Taliban in Afghanistan is the particular choice of religion. Nothing anyone has said here suggests to me that using a different religion would have any different effect here than it did there--if anything, rather confirms it would be a similar disaster.
It is interesting, that in theocratic Iran, the educational system is also shot through with religion--though they have spared the science curriculum. No doubt because they recognise you can't do nuclear physics using religious dogma