Check out page 88 of this book collecting James Madison's writings. These notes he took on Patrick Henry's VA Bill which sought to provide financial aid to "teachers of the Christian Religion." In the Memorial and Remonstrance, Madison famously argued against the content of this bill which was subsequently defeated.
In Roman numeral V of his notes, Madison ponders the question "What is Xnty?" This is relevant because only "Christianity" and not other religions were eligible for aid in Henry's bill. In V6 he discusses that some view the entire Bible as divinely inspired, some view only "essential parts" as divinely inspired; in V7 he notes some believe if a creed rejects certain key doctrines it is not Christian even if it calls itself Christian; in V8 he notes Trinitarianism, Arianism, Socinianism, (the latter two are forms of theological unitarianism) asking which of them would qualify as "Christian" under the bill; and in II6 he notes the case of "primitive Christianity," "Reformation" and "Dissenters formerly." He concludes that unless Christianity is specifically defined in the bill, judges might have to answer what is heterodoxy v. what is orthodoxy. And that in turn will "dishonor Christianity."
How this relates to theistic rationalism? As my readers know, I have found that the key Founders (certainly Jefferson, Adams, Franklin, and I would argue Washington and Madison himself) believed in what they sometimes referred to as "primitive Christianity," that was unitarian (either Arian or Socinian), which viewed the Bible as only "partially inspired," and elevated man's reason over revelation as the penultimate tool for determining which parts of the Bible were "essential" or valid. Sometimes scholars refer to this creed as a form of "Deism" (though it is not strict deism ala Thomas Paine). Dr. Gregg Frazer has dubbed it "theistic rationalism" and Madison's notes here seem to anticipate almost all of its elements.
Madison does not, unfortunately, explicitly endorse here, what form of Christianity he might believe in (though looking at his life as a whole I have concluded he was a theistic rationalist). But he did note that he did not want judges deciding whether what we call theistic rationalism is real Christianity.
If judges decided theistic rationalism, because of its heterodoxy, was not "Christianity," then it would ineligible for aid. Madison makes clear in the Remonstrance, that whatever his personal creed, he thought government aid ought to be available to all religions on a non-discriminatory basis.
Who does not see that the same authority which can establish Christianity, in exclusion of all other Religions, may establish with the same ease any particular sect of Christians, in exclusion of all other Sects? that the same authority which can force a citizen to contribute three pence only of his property for the support of any one establishment, may force him to conform to any other establishment in all cases whatsoever?
4. Because the Bill violates that equality which ought to be the basis of every law, and which is more indispensible, in proportion as the validity or expediency of any law is more liable to be impeached. If "all men are by nature equally free and independent," [Virginia Declaration of Rights, art. 1] all men are to be considered as entering into Society on equal conditions; as relinquishing no more, and therefore retaining no less, one than another, of their natural rights. Above all are they to be considered as retaining an "equal title to the free exercise of Religion according to the dictates of Conscience." [Virginia Declaration of Rights, art. 16] Whilst we assert for ourselves a freedom to embrace, to profess and to observe the Religion which we believe to be of divine origin, we cannot deny an equal freedom to those whose minds have not yet yielded to the evidence which has convinced us. If this freedom be abused, it is an offence against God, not against man: To God, therefore, not to man, must an account of it be rendered. As the Bill violates equality by subjecting some to peculiar burdens, so it violates the same principle, by granting to others peculiar exemptions.
Yet, if judges declared theistic rationalism was "Christian" and hence eligible for tax aid, it would have, by force of law, established "heresy" as Christianity. This is exactly what occurred in Massachusetts where Protestant churches received government aid under a mild state establishment. A great deal of those Protestant Congregational Churches (arguably a majority of them in Boston) receiving such aid preached unitarianism/theistic rationalism, not orthodox Trinitarian Christianity.
I'd imagine that orthodox Christians viewed this is a tremendous dignitary harm. Reader Eric Alan Isaacson, Esq., a member of the Unitarian Universalist Church, informed me that conservative Calvinists congregants actively disfellowed themselves from the unitarianian congregants.
To draw a slight parallel to a present controversial issue, also most apt in Massachusetts -- same sex marriage: Religious conservatives are asked "how is it that granting same sex couples the status of marriage harms you?" One common reply is calling something "marriage" that isn't marriage, cheapens the institution. Similarly, calling something "Christianity" (theistic rationalism/theological unitarianism) that isn't Christianity likewise cheapens the institution.
Madison's solution? Not protect Christianity by giving legal privileges to "real Christianity" only -- orthodox Christianity. But separate church and state. Perhaps then, we should separate marriage and state?