Chuck, the US Constitution as well as many state Constitutions were based on the
Massachusetts Constitution. The brain child of John Adams. In the Mass Constitution the state originally provided for the general welfare by directing the state to support houses of worship where monies were and when needed. This from a man who stated explicitly that the the USA was not founded as a Christian nation.
Now I admit I may be simplifying things a bit much, but I hope this gets the message across in a manner that does not confuse.
Constitution of the Commonwealth of Massachusetts
Article III. [As the happiness of a people, and the good order and preservation of civil government...
...Therefore, to promote their happiness and to secure the good order and preservation of their government, the people of this commonwealth have a right to invest their legislature with power to authorize and require, and the legislature shall, from time to time, authorize and require, the several towns, parishes, precincts, and other bodies politic, or religious societies, to make suitable provision, at their own expense, for the institution of the public worship of God, and for the support and maintenance of public Protestant teachers of piety, religion and morality, in all cases where such provision shall not be made voluntarily.
...
...] [Art. XI of the Amendments substituted for this].