Thank you for your response! I certainly agree that in the present day and through much of American history the church and the state have been too close for comfort, but I stand by the claim that the separation between the two is a founding principle.
One of the best voices for explaining that is Onkar Ghati, who covers the issue in detail here.
Anecdotally, many of the oft quoted founding fathers were careful to mention the importance of a government that did not interfere with the free practice of religion among the people. They also, and just as importantly, made it clear that people speaking as the government were not to play that role as well.
Here is where is gets interesting. Many states did in fact create religious structures at the state level, and that is where the tradition was fostered. I am not an attorney, but I would like to see an attorney versed in these issues discuss the incorporation of the Bill of Rights and how the tradition in the states interacts with the clear rules at the federal level.
Thank you for bearing with me as I nerd out — this is a very interesting topic. Thank you again for your response!