Religion in General a Step Towards Secularism:

Sandefur takes a jab at the notion that government can promote religion in general but not one particular religion:

This is known as the “nonpreferential” theory of the Establishment Clause. See, e.g., Patrick M. Garry, Religious Freedom Deserves More Than Neutrality: The Constitutional Argument for Nonpreferential Favoritism of Religion, 57 Fla. L. Rev. 1, 3 (2005) (“the Establishment Clause aims to keep the government from singling out certain religious sects for preferential treatment, but it does not prevent the government from showing favoritism to religion in general.”)

The problem is that there is no such thing as “religion in general.” Certainly there is no way of demarcating the things that separate “religion in general” from “non-religion” in a way that makes consistent sense to sectarians. Is belief in the trinity “religion in general” or is it just sectarian? What about belief in the divinity of Christ? It’s easy to say that the first thing is just sectarian because we’re used to seeing Protestant sects that don’t believe in the trinity. But what about the latter? If even atheists can be Quakers, surely someone who doesn’t believe in Christ’s divinity can still be a Christian…no? I don’t think so, but who am I to be making such distinctions about another person’s religious beliefs? And if we can’t draw that line, then the idea of government endorsing “generic religion” is an invitation to just the sort of religious controversies that the First Amendment was designed to keep out of government.

Similarly, Thomas West reaches the same conclusion but for the other side of the religion v. secularism debate:

Hamburger does a good job showing that any idea of government support of "religion in general" is an illusion. There is no such thing as "religion in general." All meaningful government support of religion is always support of a particular religious view, as 19th-century Catholics bitterly experienced. Today, support of "religion in general" would include taxpayer funding of Wiccans, Satanists, Muslims (including those who teach hatred of America), and worshippers of that favorite goddess of some feminists, "Our Sweet Sophia."

The problem for West is that, as a hagiographer of America's Founders, he hasn't resolved the dilemma that this is exactly what they believed in: "religion in general" not "Christianity," or "Judeo-Christianity" exclusively. Indeed his article notes:

That is why in spite of their differences on the "establishment of religion" question, Jefferson, James Madison, John Adams, and George Washington could all agree on this provision of the Northwest Ordinance, passed in the same year as the First Amendment: "Religion, morality, and knowledge, being necessary to good government and the happiness of mankind, schools and the means of education shall forever be encouraged."

Likewise Washington's Farewell Address invokes this amorphous concept of "religion in general":

Of all the dispositions and habits which lead to political prosperity, religion and morality are indispensable supports....And let us with caution indulge the supposition that morality can be maintained without religion. Whatever may be conceded to the influence of refined education on minds of peculiar structure, reason and experience both forbid us to expect that national morality can prevail in exclusion of religious principle.

Now, many back then and today probably thought Washington meant "Christianity." But the problem is that's not what he said or what he meant. Washington meant "religion" in general. And "sound religion," [what West refers to when he writes "all sides agreed that the right kind of religion was vital for the success of republican government,"] included not just Christianity, but Judaism, Deism, Unitarianism, Hinduism, Islam, pagan Greco-Romanism, and Native American Spirituality. The "right" kind of religion meant it was liberal in the classical (not modern) sense of the term: It was voluntary and didn't believe in conversion by the sword.

In invoking "religion in general" the Founders drew a very low lowest-common-denominator that equated "religion" with any system that taught an overriding Providence and a future state of rewards and punishments which, they believed, virtually all world religions did. Hence, the Founders' notion of "religion in general" converged with their amorphous, undefined God of the civil religion, which attempted to be all things to all believers.

As Benjamin Rush put it (and keep in mind, I don't believe Rush was a theistic rationalist like the other key Founders but rather was a Trinitarian Universalist who denied eternal damnation):

Such is my veneration for every religion that reveals the attributes of the Deity, or a future state of rewards and punishments, that I had rather see the opinions of Confucius or Mahomed inculcated upon our youth, than see them grow up wholly devoid of a system of religious principles. But the religion I mean to recommend in this place, is that of the New Testament.

I have no problem with government promoting the notion of "religion in general" as long as it's understood to mean a diversity of Christian and pagan, orthodox and heterodox religions, all of them taking their rights equally under the law. This is I think what Madison had in mind when he proposed setting up factions against one another that would "cancel" each other out. [And I think atheism and secular interests also ought to have equal rights with the religious factions.]

As Gary North put it, discussing Madison's desire for religious factions:

It is well known that Madison’s greatest fear was his fear of the triumph of any particular political faction. Federalist 10 is devoted to his theme. What Madison wanted was political neutrality: a world of politically impotent factions, only as strong as necessary to cancel out each other. In the 1787 “Vices” essay, he inserted this conclusion immediately following the paragraph on state religious oaths: “The great desideratum in Government is such a modification of the sovereignty as will render it sufficiently neutral between the different interests and factions, to controul one part of the society from invading the rights of another, and at the same time sufficiently controuled itself, from setting up an interest adverse to that of the whole Society.”7

[...]

He said this explicitly in Federalist 51: “In a free government, this security for civil rights must be the same as for religious rights. It consists in the one case in the multiplicity of interests, and in the other, in the multiplicity of sects. The degree of security in both cases will depend on the number of interests and sects; and this may be presumed to depend on the extent of country and number of people comprehended under the same government.”9

North, as a theocrat, rightly notes that setting religious factions against one another to cancel each other out, was a quasi form of secular humanism and gravely conflicts with the "Christian Nation" ideal. The Founders' philosophic ideal of "religion in general" that granted equal rights to all [even non-"Judeo-Christian"] religions, which led to a multiplicity of diverse religious sects, offsetting one another is not quite what today's secular humanists desire. Rather this reflects their unitarian ideal of Founding era classical humanism.