The US of A

Mark David Hall: Did America Have a Christian Founding?

Yes. Christianity was an essential component.

In 1776, every European American, with the exception of about 2,500 Jews, identified himself or herself as a Christian. Moreover, approximately 98 percent of the colonists were Protestants, with the remaining 1.9 percent being Roman Catholics.

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[...] it is important to note that nominal Christians might be influenced by Christian ideas, just as it is possible for an orthodox Christian to be influenced by non-Christian ideas. I believe that an excellent case can be made that Christianity had a profound influence on the Founders.

Greek democracy + Roman Law + Christianity + English people = USA

Also, it's not true that the Founders wanted purely secular governments.

Simply put, the Founders were creating a national government for a very few limited purposes—notably those enumerated in Article I, Section 8. There was almost universal agreement that if there was to be legislation on religious or moral matters, it should be done by state and local governments.

Yup. The Founders restricted the power of the federal government. The states, however, were free to utilize religion in their legislation.

In fact, states remained active in this business well into the 20th century. It is true that the last state church was disestablished in 1832, but many states retained religious tests for public office, had laws aimed at restricting vice, required prayer in schools, and so forth. Because the federal government was not to be concerned with these issues, they were not addressed in the Constitution. The First Amendment merely reinforced this understanding with respect to the faith—i.e., Congress has no power to establish a national church or restrict the free exercise of religion.