From Noah Feldman’s Divided by God:

The revolutionary American idea that the people were sovereign profoundly disturbed the old model: How could the state establish the religion of the sovereign if the sovereign people belonged to many faiths? The framers rose to the occasion. For the first time in recorded history, they designed a government with no established religion at all.

… The early republic was religiously diverse in that it was inhabited by several different Protestant denominations. This “multiplicity of sects,” as James Madison brilliantly realized, ensured that no one denomination had the capacity to establish its own state religion at the national level.

… The dominant idea organizing church-state relations in the framers’ era was the liberty of conscience, understood to protect religious dissenters-representing the religious diversity of the time-against compelled taxation to support teachings with which they disagreed.

…In America, the establishment of religion by the government came to be seen as posing a fundamental danger to the liberty of conscience by threatening dissenters with the possibility of coercion. The constitutional guarantee of nonestablishment sought to protect conscience from coercion by guaranteeing a division between the institutional spheres of organized religion and government.