The first amendment more or less mandates it. As John Marshall said in another context, "the power to tax is the power to destroy." Taxing religious organizations, it can be argued, could be a way to limit their ability to proseletyze or carry out their religious mission. Basically, free exercise, protected in the First Amendment, would be jeopardized by allowing government the power to tax religious organizations.

They are exempt from taxation because we believe that what they are doing is valuable to society.  We think that religions help to bind members of our society together more closely and we think that they make us better people.  Since we approve of them, we do not want to tax them.