I think that religion should be taught a form of history, using textual analysis, anthropological findings, and using comparative chronologies to verify reported events.
For example, I just saw a PBS Documentary called, “The Secret Family of Jesus,” which discussed the findings of some recently discovered graves on the Mount of Olives. These contained the ossuaries (bone boxes) of Jesus’ relatives (and even one box marked Jesus). Apparently, there is a whole untold story here about St. James and the part of the Jesus movement that never broke off from Judaism. James was the first Christian bishop, and his faction considered themselves both Jews and Christians—just as Jesus had. They believed that gentiles would have to convert to Judaism (and be circumcised) in order to join the Jesus movement.
However, in a fateful meeting between between St. Peter and St. Paul it was decided that such conversion would be unnecessary (because Jesus would be coming back any day). St.Paul, who had never met Jesus, claimed to have regular conversations with him (which we now recognize as likely to have been temporal lobe epileptic seizures). St. Luke appears to have sided with St. Paul and his accounts come down to us as a very selective history which more or less writes James out of the picture.
James’ faction consisted of Jesus’ extended family and the families of his disciples centered on the Jerusalem Church. James was in charge of this Church for 30 years while he was alive, and it persisted for 50 years after his death. In this Church, Jesus was considered a prophet and a man, and his message of love was couched in terms of freedom from oppression. The face of Christianity (which became stridently anti-Jew) would have been considerably different, had this faction not been muscled aside by St.Paul, who had large numbers of gentile converts on his side.
I think a similar treatment of Islam would be illuminating. Muhammad also experienced temporal lobe epileptic seizures, during which he believed himself to be taking dictation directly from God. Much of the development of Islam from that point forward can be traced to errors, omissions and contradictions in what he wrote down. For example, he failed to name a successor, or provide a method by which a successor could be chosen, so that the whole of Islam would be thrown into civil war every time there was a major succession issue.
If religion were taught from an outsider’s perspective like this, I think it would probably do some good—if you could get people to sit still for it. Unfortunately, any such attempt would send believers into a frenzy of denial, and if history is any guide, they would turn to politics and use every underhanded means possible, to take over the government in order to force the teachers to teach the religious view. If they should succeed, that would be a real calamity. It is probably better to teach Critical thinking skills and leave it at that.