Myth:
The Northwest Ordinance provides for the support of Christianity and demonstrates that the authors of the Constitution did not believe in strict separation.
Background
Opponents of church/state separation cite the Northwest Ordinance to prove that the authors of the Constitution didn't believe in strict separation of church and state. Enacted in 1787 under the Articles of Confederation then again in 1789 under the Constitution, the Northwest Ordinance established a governing structure for the Northwest Territory from the Great Lakes down through the Ohio river valley. Accomodationists say that it also provided for the public funding of religion.
The first sentence of Article III states:
Religion, morality, and knowledge, being necessary to good government and the happiness of mankind, schools and the means of education shall forever be encouraged.
According to accommodationists and others opposed to the strict separation of church and state, this statement demonstrates a number of things. At the very least, Congress at the time supposedly didn't have a problem with government support of religion, religious beliefs and religious organizations. It is also often claimed that politicians of the time must have considered a given that "good government" required the presence of religion.
David Barton, an accommodationist who is quite fond of myths like these, has even argued that:
Since the same Congress which prohibited the federal government for the "establishment of religion" also required that religion be included in schools, the Framers obviously did not view a federal requirement to teach religion in schools a violation of the First Amendment. (The Myth of Separation)
Response
This argument sounds superficially plausible, but there are several key problems with it. This may be why most of those who try to use this argument don't go any further than quoting the Northwest Ordinance, assuming that it speaks for itself and requires no further explanation. If they did try to make an argument based on it, though, they might realize just how weak their position is.
First, there is no evidence that anything at all was done on the authority of this sentence. There is no evidence, for example, of anyone transferring money from the government to any religious groups and citing this passage as the basis for it. Indeed, Article III in its entirety seems to have failed to actually cause anything to happen — not surprising, since it reads like one long rhetorical flourish which was not designed to enact anything specific in the first place. If this passage really meant what accommodationists claim, why did government support for religion never materialize? It's more reasonable to conclude that the author had something else in mind.
Second, the Northwest Ordinance was created in part to structure dealings with the native Americans of the region. These tribes were considered foreign nations by and, as such, relations with them were not covered under the First Amendment (or the rest of the Bill of Rights). Because of this, it cannot qualify as a violation of the letter of a strict separationist reading of the Constitution and certainly not as precedent for domestic government spending to support religion.
Third, it is questionable whether or not the Northwest Ordinance was ever a valid law. It was originally passed when Congress was operating under the Articles of Confederation — a document which did not grant them authority to pass such legislation. Even when reenacted under the Constitution, it is arguable that where it conflicted with the Constitution, the Constitution was superior and the Ordinance was invalid — just as any law passed today which contradicts the Constitution is invalid.
Fourth, The Northwest Ordinance was enacted eight days before the First Amendment was even first proposed by James Madison, never mind added to the Constitution. Accommodationists rely heavily on the idea that the Northwest Ordinance was reenacted by the same Congress which passed the First Amendment, but this order of events hurts their case more than it helps because they are trying to argue that the Northwest Ordinance contradicts the separationist reading of something which hadn't even been considered yet. We cannot assume that those who voted for the Ordinance had the First Amendment in mind at the time, and therefore it cannot be used as a basis for inferences about their beliefs as to what the First Amendment meant.
Fifth, an earlier form of the Northwest Ordinance had a different version of this passage which would have explicitly provided for the government support of religion. Thomas Jefferson originally wrote the Northwest Ordinance, and some anti-separationists try to make much of this, ignoring the fact that his original draft was completely secular in nature. Later, the following addition was proposed:
Institutions for the promotion of religion and morality, schools and the means of education shall forever be encouraged.
If it had passed in this way, the Northwest Ordinance would indeed do a lot that the accommodationists claim. Because the wording was changed, though, it's far more reasonable to conclude that people regarded such explicit government support of religion as inappropriate. They didn't return to Jefferson's fully secular version, but they changed enough. Had Congress really intended for the government to aid or encourage religion in any way, this phrasing would have expressed that intent; by adopting what was actually passed, they instead demonstrated that this was not their intention at all.
Finally, the anti-separationist position is predicated upon the idea that whatever the First Congress did was necessarily constitutional. This premise is completely wrong. Many measures passed by the First Congress were fiercely contested — the Sedition Act of 1798, for example, was certainly unconstitutional. Just because they thought they were doing something constitutional doesn't mean that we, too, must agree.

