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.
First Joseph Story may have been an authority; but he was not *the* authoritative source for the First Amendment. He had nothing to do with its drafting and ratification. My friend Phillip Munoz of Notre Dame (and Princeton), who is about as authoritative a modern scholar of the F.A. as it gets, compared Joseph Story's commentaries to the actual sources of the drafting and ratification of the First Amendment and concluded Story misreads the Founding record. Similar to how scholars sympathetic to the secular left "read in" Jefferson's and Madison's "Virginia view" to define the meaning of the religion clauses, Story unfairly reads in the "Massachusetts' view."
Now, Story's quotation about the First Amendment being concerned, generally, with Christianity, not other religions, may shed light on the underlying aim of its religion clauses (which, in turn, may have had multiple underlying aims). However, it still cannot trump the TEXT of the Constitution, which uses the term "religion" not "Christianity."
This is an aside: I want to make sure we don't fall into the Christian Nationalist trap of concluding the First Amendment somehow was meant to cover, privilege or establish "Christianity generally," but not other religions. We all agree that, as originally conceived, the FA applied to the Federal government only. Whether the EC can be "incorporated" demands synthesizing evidence from the framing of the original bill of rights (late 18th Cen.) with the 14th Amendment (mid 19th Cen.). Munoz has concluded that, unlike the Free Exercise Clause, the Establishment Clause is impossible to incorporate. He may be right; however, as Akhil Amar argued, the original Equal Protection Clause -- which would demand government treat Christianity equal with Islam, Judaism, and other religions -- could do quite a bit of what SCOTUS currently has the Establish Clause doing.
Next, I want to clarify what it means to say the F.A. is undergirded by "Protestant Christianity." I argue that a "Protestantism" but not necessarily "Christianity" undergirds the notion of religious liberty. Protestantism meaning "to protest" or "dissent." The idea of freedom from ecclesiastical, authoritative interpretations of the Bible, most notably freedom from the Magisterium, but also freedom from non-Roman ecclesiastical authoritative teachings. Taken to its extremes -- which America's Founders did -- this means freedom from the very creeds that define the essence of what it means (historically, to many folks) to be a "mere Christian."
I wrote about this implicit Protestant establishment here. I quoted Nathan Hatch, president of Wake Forest University and one of the premier scholars of Religion and the Founding Era, describing the theology of Charles Chauncy, a key theological influence on the American Founding:
Charles Chauncy, pastor of Boston’s First Church for sixty years (1727-1787), is the most prominent example of an exclusive appeal to Biblical authority in order to unravel theological orthodoxy. Chauncy was persuaded to emphasize Bible study by reading the works of English divines, such as Samuel Clarke’s The Scripture-Doctrine of the Trinity (London, 1712) and John Taylor’s The Scripture-Doctrine of Original Sin (London, 1740). Both authors used a “free, impartial and diligent” method of examining Scripture to JETTISON, respectively, the doctrines of the Trinity and of Original Sin. 
During the 1750s, after the Great Awakening, Charles Chauncy spent seven years engaged in the approach to Bible study expounded by these English authors. In the spring of 1754 he wrote to a friend,
“I have made the Scriptures my sole study for about two years; and I think I have attained to a clearer understanding of them than I ever had before.”
His studies led him to draft a lengthy manuscript in which he REJECTED the idea of eternal punishment and embraced universalism.
Now, I point this out because terms need precise meaning. Perhaps I am being pedantic in claiming a "Protestant" but not necessarily "Christian" political-theology; but when some/many folks see terms like "Protestant Christian" or "reformed Christian" they sometimes improperly "load" or "read in" things. If "Protestant Christianity" can unite a Chauncy with a Calvin against Rome's monopoly on biblical interpretation, then the term is apt. However, to some/many, "Protestant Christianity" excludes Chauncy. And that's not what America's Founding political theology was all about. Perhaps I attack strawmen here. But my co-blogger to whom I respond has cited American Vision authoritatively. And it's precisely these folks who engage in such a misreading of the American Founding's political theology.
To them "reformed Protestantism" means Sola Scriptura, orthodox Trinitarianism, and TULIP. The "political Protestantism" of the American Founding does not necessarily include any of this. Again, it's something that can unite a Chauncy with a Cavlin, a Jefferson with a Henry (both Anglicans), the unitarian John Adams with his trinitarian cousin Sam (both Congregationalists).
Indeed even Joseph Story who seems a key figure for the "Christian Americanists'" attempt to read in a common law "general Christianity" to the American Founding was a biblical unitarian-universalist, and hence "not a Christian" according to minimums that "Christian Americanists" adhere to for what it means to be a "Christian."
And that highlights the problem with trying to argue some kind of "Christianity generally" was to be privileged by the American Founding. In order to privilege "Christianity generally" you had to agree on certain minimums of what it meant to be a "mere Christian" eligible for such privilege. As James Madison argued in his notes for the Memorial and Remonstrance, that was a task impossible for politics.
Finally, I note the idea of religious and political liberty as authentically reformed Protestantism is debatable. Calvin had Servetus put to death for denying the Trinity. The Puritans certainly didn't recognize religious liberty, but rather enacted a theocratic code that demanded the death penalty for, among other things, worshipping false gods. And when the proto-Baptist Roger Williams articulated his novel ideas on liberty of conscience, the dominant view of reformed Protestants/Calvinists reacted to Williams' ideas like Dracula does to a cross.