The Founders were Christians who formed their vision on principles espoused by the likes of Locke and Montesquieu. The concept of the freedom of religion has its origins in Native American philosophy courtesy of Roger Williams, who introduced the distinct separation of the state from religion.
Williams was banished from Massachusetts Bay Colony in 1635, which caused him to live with Native Americans, where he became familiar with their concept of religious tolerance. Roger, having formed his own philosophy, established a strict adherence to a state free from religion when he founded Providence.
Later, other colonies adopted the philosophy of a state separate from religion, and the concept was systematized as US doctrine with its adoption in the Bill of Rights.
The US government was not founded as a Christian state, but rather one free from religious influence. That is the Founders' vision of the freedom of religion. We are free from government interference in our practice of religion, at the same time the government is to be free from religious dominion over it.