As I noted previously, I think Judge Michael McConnell of the 10th Circuit Court of Appeals one of the best Establishment Clause scholars. And he shows off his talent in his most recent opinion. I'm not going to analyze the ins and outs of his Establishment Clause jurisprudence (you have Eugene Volokh for that). Rather, how the passage from the opinion well illustrates the impossibility of America being a "Christian Nation" in a civil governmental sense:
CCU stated that its students, faculty, and trustees are not of a single religion, because the school is an interdenominational institution; it “unites with the broad, historic evangelical faith rather than affiliating with any specific denomination.” The state defendants took a different view: to them, all Christians are of the same religious persuasion, and denominational distinctions do not matter. The “correct” answer to that question depends on one’s ecclesiology. But under the First Amendment, the government is not permitted to have an ecclesiology, or to second-guess the ecclesiology espoused by our citizens. “Courts are not arbiters of scriptural interpretation.”
The State defendants blithely assumed that they could lump together all “Christians” as a single “religion.” But the definition of who is a “Christian” can generate an argument in serious circles across the country. Some students at CCU are members of the Church of Jesus Christ of Latter-Day Saints, or “Mormons.” Members of the LDS Church stoutly insist that they are Christians, but some Christians, with equal sincerity and sometimes vehemence, say they are not. In order to administer Colorado’s exclusionary law, government officials have to decide which side in this debate is right. Similar questions plague the religious taxonomy of Jehovah’s Witnesses, Christian Scientists, Unitarian-Universalists, various syncretistic groups and even (in some circles) the Roman Catholic Church.
To make matters worse, the Commission has (no doubt without animus) applied different standards to different religious traditions. When confronted with the question of whether Regis College was eligible for student scholarships, the Commission (and later the Colorado Supreme Court) focused on the particular denomination, which is Roman Catholicism, and concluded that the institution was eligible. In CCU’s case, however, the Commission focused on a broader category: all Christians....
The reason why government cannot give religious rights to "Christianity" is that it would have to define "Christianity" which -- according to the unalienable rights of conscience -- it may not do. So government can give rights to "religion" and say you can't prohibit its free exercise, establish it or discriminate among "religions," but cannot give rights to Christianity only. This is what Madison's notes on the Memorial and Remonstrance discuss.
If government did for instance, say we'll support Christianity or the "Christian sects" only then the inevitable questions arise: Do Mormons have rights under this doctrine or are Mormons not Christian? What about those "Christian" Churches that are marrying same-sex couples? Are they real "Christians"? What about "Jehovah’s Witnesses, Christian Scientists, Unitarian-Universalists, various syncretistic groups and even...the Roman Catholic Church?"
Many evangelicals who promote the "Christian Nation" thesis devoutly believe that these religions are not "Christian," that Christianity = orthodox Trinitarianism, the Bible is infallible, etc. I know a few of them who wish to draw the line there (i.e., Christianity = orthodoxy and that's the only type of religion that should receive public support or the public's imprimatur). Some of them are more generous in regard to what they might presently permit, but insist that this is how America was founded.
I know this might sound a little "strawmanish" -- who is it that argues Christianity only should receive "rights" or that the EC was initially conceived to protect Christianity only? It's not just Barton et al. Justice Rehnquist in his dissent in Wallace v. Jaffree intimated this was the original understanding of the Establishment Clause. And Clayton Cramer, who is a respectable historian of the hard conservative bent has intimated the Establishment Clause as originally conceived protected Christian sects only from government discrimination.
The problem is the key Founders were not orthodox Trinitarian Christians (what many folks regard as the only "true" Christianity) and when they said for instance "religion" provides republican government with vital moral support, they did not mean biblical orthodox Trinitarian Christianity exclusively. Indeed they purposefully chose to give federal constitutional rights to "religion" not "Christianity."
One of the most notable quotations that seems to support the "Christianity only" view of constitutional rights comes from Justice Joseph Story, indeed, was cited in Justice Rehnquist's dissent.
§ 1871. The real object of the amendment was, not to countenance, much less to advance Mahometanism, or Judaism, or infidelity, by prostrating Christianity; but to exclude all rivalry among Christian sects, and to prevent any national ecclesiastical establishment, which should give to an hierarchy the exclusive patronage of the national government.
Two points: One, Story is explicating the "real object" or underlying aim of the First Amendment. I don't doubt the real aim was indeed to exclude rivalry among the sects, just about all of the major ones of which called themselves "Christian." However, the text of the First Amendment is what controls and the text protects "religion" not "Christianity."
Secondly, Story himself was a Unitarian, a biblical Unitarian of the Socinian variety who believed Jesus a man, not at all divine, but on a divine mission. And he fervently argued that his system -- quite popular in Mass. during his time -- was true, authentic Christianity.
So even if we take Story's understanding as dispositive, we have to conclude that Socinianism -- that which denies the Trinity -- is "Christianity" protected under the First Amendment. Further, in protecting "Christianity" only government has now concluded that Socinianism, that which the orthodox regard as utter heresy, merits the label "Christian." And that is something that the government cannot, by right, do. If government, rather, protects "religion" in general, the problem is solved.