What is Religion?
In order to assess whether the Founders believed "religion should have no place in government," we should first understand what is meant by "religion." If by using the term "religion," one is simply making the case that the U.S. government should not endorse Catholics over Protestants (or vice versa) or establish a state church, then such a case is definitely consistent with the Constitution, the Bill of Rights, the Virginia Statute for Religious Freedom, and the eventual consensus of the American Founders. If, however, "religion" is broad enough to include belief in God in general as well as an official acknowledgment that our rights come from God and that we are accountable, in some way, to God, then we're talking about something else entirely.
Religious Belief is Inevitable
Part of the definition of religion, according to Dictionary.com, is "a set of beliefs concerning the cause, nature, and purpose of the universe." By this broad definition, humanism would certainly qualify as a religion. In fact, by this definition, every single human being possesses some type of "religious" view, because we're talking more about worldview than about the embracing of a specific supernatural entity.
A quote attributed to Noah Webster affirms this point. Webster is alleged to have said: "Every civil government is based upon some religion or philosophy of life." In researching this article, I was unable to find a primary source for this quote, so I can't confirm that Mr. Webster actually said it. Whether he did or not, though, I think it's an accurate statement. Every civil society that has ever existed is shaped by philosophical and religious assumptions.
The Founders Embraced Judeo-Christian Monotheism
It is a matter of historical fact that the Founding Fathers of the United States of America fully embraced monotheism, and their monotheistic framework was shaped primarily by a culture steeped in Judeo-Christian belief and tradition. And this Judeo-Christian monotheism was not incidental or peripheral to their efforts in erecting the United States. It was a worldview that was front and center, and was incorporated fully into the foundation of our Republic. One need only look to the colonial charters, the Declaration of Independence, and the state constitutions to confirm this.
It is factually incorrect to associate the view that "religion should have no place in government" with the Founding Fathers of the United States. It certainly wasn't George Washington's view, who declared in his Inaugural Address that the people of the United States were "bound to acknowledge and adore the Invisible Hand which conducts the affairs of men more than those of the United States." Washington issued the first national Thanksgiving Proclamation after the U.S. Constitution, and said it was the "duty of all nations" to acknowledge God with worship and gratitude. And it was Washington, in his Farewell Address, who said that "religion and morality" were "indispensable" to "political prosperity." Doesn't sound like a guy who wanted religion completely separate from government. And, if I may, who are we to disagree with George Washington when it comes to discussing the original meaning of the Constitution or the intentions of our Founders?
Then, of course, there's Jefferson, who secularists love to quote as someone who promoted the separation of church and state. While Jefferson most certainly opposed anything that smacked of a Church of America, he nevertheless had no problem with Judeo-Christian monotheism being at the center of our Republic. Consider his famous question: "And can the liberties of a nation be thought secure when we have removed their only firm basis-a conviction in the minds of the people that these liberties are the gift of God?" That sounds like a question of a religious nature to me.
The Declaration of Independence makes it clear that the Founders believed in the existence of God and that our fundamental rights come from God. These are religious sentiments and they are enshrined into our founding document and, by consequence, our heritage and identity.
It's the right of the American people today to decide to jettison the beliefs of the Founding Fathers. They would be wrong to do so, but it's their legal right. People are entitled to their opinions, but they are not entitled to their own facts. It's legitimate to disagree with the Founders, but it's not right to redefine the values and beliefs of the Founders. On the issue of religion and government, the Founders have a right to speak for themselves, and they have done so.