This vastly misstates the reasoning behind the Establishment Clause. Contrary to common belief, there simply was no goal to fully cleave government and religion, at least at the level of state government. There is plenty of scholarship on the point, but to put it in brief, the Establishment Clause was included to provide comfort to the states that no FEDERAL religion would be established that would supersede various religions that were already proscribed via various STATE constitutions — and this was needed to get the requisite number of states to ratify the Constitution.
Have a look: http://www.constitution.org/primarysources/state.html
Many states already required Christianity, and some even required a declaration of a Protestant faith at best. Consider the conflict between the Baptists and the Anglicans of Virginia in this situation.
States weren’t constitutionally barred from establishing religions until after the ratification of the Fourteenth Amendment.