That is not the original bargain. The decision to not recognize a state religion was a part of US political policy from very early times. In 1797, the treaty of Tripoli stated "The Government of the United States of America is not, in any sense, founded on the Christian religion." The decision to grant churches tax exemption comes much later and involves quite a bit of back and forth at the federal and state level. Though, to be fair, there has always been quite a bit of not-officially-ratified tax leniency on churches, even before federal laws were passed.