The First Amendment was meant, as Justice Joseph Story says, to level all Protestant religions with each other, but not to equalize Christianity with Judaism and Islam. Alternatively, it did level all religions, even Judaism and Islam. But either way, it was only on the federal level. The real purpose of that amendment was merely to protect the state established churches from federal interference. Thomas Jefferson's letter of 23 January 1808 to Samuel Miller evinces a similar view. Therefore, the notion of incorporating the First Amendment onto states is absurd. Some of the men who ratified the First Amendment, actually believed in full religious liberty. Others, however, were merely jealous for their state established churches. So how the hell do you incorporate that into the states via the 14th Amendment?
Now then, if you read works of those who believed in full religious liberty (as opposed to merely jealously protecting the state church), works like John Locke's "A Letter Concerning Toleration," James Madison's "Memorial and Remonstrance Against Religious Assessments," Thomas Jefferson's The Virginia Act For Establishing Religious Freedom", Jefferson's Notes on the State of Virginia (s. v. "Query XVII"), and John Leland's The Rights of Conscience Inalienable; and therefore Religious Opinions not cognizable by Law: Or, The high-flying Churchman, stript of his legal Robe, appears a Yahoo, you'll see the following: that the justification for all these men, was based on the principles of Protestant Christianity. The underlying principle among them all, is that religion is within the jurisdiction and sovereignty of God alone, that no man on earth (whether pope or government official) has the authority to make laws regarding religion. Every man has the freedom to believe whatever he wants, and no man has the right to force him otherwise. The intent of religious liberty, according to these men, is to give all men the ability to worship God freely. In fact, John Locke and James Madison even say that an atheist has no right to religious freedom, because he doesn't believe in the God who granted that freedom in the first place. Similarly, Thomas Jefferson said elsewhere, "God who gave us life, gave us liberty at the same time. Can the liberties of a nation be secure when we have removed their only sure basis, a conviction in the minds of the people that those liberties are the gift of God?" For all these men, religious liberty was a Protestant Christian principle, viz. the opposition to popery, and the freedom of every man to read the Bible for himself and come to his own conclusion. If the First Amendment enshrines religious liberty (which is doubtful, as I show above, regarding states v. the federal government), then the First Amendment is itself a Christian document.
(In my humble opinion, if we extrapolate, we'll see that the concern of being allowed to worship God freely, applies to other areas of life as well, besides religion. If men must be free to worship God, without being compelled to join foreign religious and perform strange rituals not to their liking, does this not also mean that men must not be compelled to believe in or practice other ideologies, such as communism? The Framers spoke of religion alone, merely because religion was the ideology, par excellence. But if you read their concerns, you'll see that their concerns apply generally to all ideologies, not only religious ones. Why should I be forced to subsidize (with my taxes) a public school that teaches doctrines not to my liking? How is that different than forcing me to subsidize a church not to my liking?)
Returning to religious liberty being a Christian concept, in fact, James Madison explicitly credits Martin Luther in his letter of 3 December 1821. Madison is referring to Martin Luther's doctrine of the two kingdoms, in which the state possesses a temporal sword to punish crime and violence, and the church possesses a spiritual sword to punish heresy and inculcate orthodoxy, and neither may infringe on the other's jurisdiction. Both, however, are subordinate to God. Therefore, under Luther's doctrine, the state is separate from the church, but is still subordinate to God and subject to His commands. Christianity is binding on the state no less than on the church, only a different subset of the laws of Christianity is applicable to each, according to the station assigned by God. (Similarly, the fact that only kohanim (priests) can offer qorbanot (sacrifices), does not mean that everyone else is "secular.")
(In my humble opinion, when Locke, Madison, Jefferson, and Leland say that the state can have no jurisdiction over religion because men have not delegated to the state that power under the social contract, and that furthermore, they cannot, as religion belongs to God alone and cannot be delegated to anyone else (nemo potest dare quod non habet - one cannot give that which he does not have), it seems to me that what they are doing is, is giving a justification for Luther's doctrine. Luther distinguishes between the two kingdoms, but Locke et. al. are, I believe, offering a social contract theory-based justification for Luther. Given that it was Reformed Christians who are largely responsible for the invention of social contract theory, in the form of federalism, it seems fitting that Luther be justified based on a secular offshoot of Calvinism.)
So in fact, according to Madison, the morality of the United States's laws was to be a Christian morality. Again, the First Amendment was merely meant to equalize all Protestant sects with each other, but Christianity in the abstract was still to be supreme. The morality of the laws was to be an exclusively Christian one. There was to be no established church, enforcing dogma and ritual, but the state was still to enforce Christian morality. In fact, the First Amendment is very precise, speaking of a religious "establishment," and Jefferson speaks of the separation of "church" and state; the words "establishment" and "church" (as opposed to "religion") are chosen very deliberately, to refer not to religion or Christianity in the abstract, but rather, to concrete entities, to structured organizations. The First Amendment forbids the favoring of a church establishment (Baptist, Anglican, Congregationalist, Presbyterian), but not the favoring of Christianity in the abstract. No wonder that James Madison said, in a letter of 1833 to Jasper Adams, "I must admit...that it may not be easy, in every possible case, to trace the line of separation, between the rights of the religious and civil authority, with such distinctness, as to avoid collisions and doubts on unessential points." (Quoted in John Eidsmoe, Christianity and the Constitution: The Faith of our Founding Fathers (Grand Rapids, MI: Baker Book House, 1987), p. 110.) That's why even people like Thomas Jefferson and James Madison could issue Christian thanksgiving proclamations, calling for repentance and prayer to God. (Clarification: As Jefferson shows, in letter to Samuel Miller, he did not issue thanksgiving day proclamations as President of the United States. However, as Governor of Virginia, he did issue such proclamations. Evidently, Jefferson considered the First Amendment merely a technical legal impediment, but still felt that theoretically, the issuing of religious proclamations was legitimate for the government. On the state level, where no legal restriction existed, he was free to pursue this. This is all the more interesting, given that Jefferson himself authored the "The Virginia Act For Establishing Religious Freedom." Now, that act was not yet in effect when Jefferson was governor, but presumably, he still believed in its tenets. So apparently, Jefferson felt that while the First Amendment forbade the issuing of thanksgiving proclamations, by contrast, the not-yet-legislated "The Virginia Act For Establishing Religious Freedom," authored by him himself, no less, did not. So it is difficult to imagine how on earth we could incorporate the First Amendment via the Fourteenth, when apparently, the First Amendment was of such a peculiar character, limited to the federal government, and intended, according to some, to merely protect the state established churches from federal interference, and intended, according to Jefferson, to be legally more onerous and restrictive than what was morally necessary and proper for the states. Oh, and on the same day that Jefferson and Madison submitted their "The Virginia Act For Establishing Religious Freedom" - which Jefferson authored, and which Madison defended and advocated for with his "Memorial and Remonstrance Against Religious Assessments," the two being partners in the endeavor - James Madison also submitted a "Bill for Punishing Disturbers of Religious Worship and Sabbath Breakers." Just as Jefferson felt there was nothing wrong with issuing religious proclamations, Madison thought there was nothing wrong with punishing Shabbat desecrators. )
Thomas Jefferson, in his famous letter to the Danbury Baptists, speaks of the "wall of separation between Church & State." Now, writing to the Baptists, it makes sense that Jefferson made a reference to Roger Williams, who said, "...when they have opened a gap in the hedge or wall of separation between the garden of the church and the wilderness of the world, God hath ever broke down the wall itself, removed the candlestick, and made His garden a wilderness, as at this day. And that therefore if He will eer please to restore His garden and paradise again, it must of necessity be walled in peculiarly unto Himself from the world..." We should notice three things: (1) Jefferson is relying on Roger Williams, so Jefferson's doctrine of the separation of church and state is obviously a Christian one; (2) the purpose of the wall is to protect the garden of the church from the wilderness of the state, with the threat being not that the church will corrupt the state, but the opposite, that the state will corrupt the church; (3) the church is to be kept peculiarly unto God, which is the same concern we saw earlier, that religion is something that only God, not the state, has jurisdiction over.
In my opinion, the Framers' political philosophy, regarding religious liberty, tended towards libertarianism, but their moral philosophy was always a Christian one. Libertarianism is merely a political philosophy, and can be paired with any moral philosophy. Ayn Rand chose Objectivism to accompany her libertarianism, while the Framers chose Christianity. Myself, I am a libertarian and tends towards the most separatist and radical view of separation, that the state should have nothing whatsoever at all to do with religion, believing that the truth is strong enough on its own, and believing that the state has no jurisdiction in such areas. (I also believe that public schooling is unconstitutional and illegal.) But the First Amendment means what it means, whether I like it or not.