In broad brushes I agree with Daniel Larison:
One of the things that always bothered me about George Bush’s revolutionary rhetoric was how he identified the expansion of political freedom with God’s design for man, which makes God’s plan one of narrow political deliverance rather than deliverance from death. These claims that representative government and separation of powers have some grounding in Christianity bother me in a different way. Probably the most thoroughly Christianized state in the medieval world was Byzantium, but it retained a late Roman autocratic system of government for its entire existence, so what is the connection between political structures and Christianity? Because the experience of most of Christian history in most parts of the world does not fit this picture of Christianity as the foundation of modern constitutional government, these claims have to privilege the Christianity of certain parts of western Europe and North America as the norm when it was clearly the exception. Furthermore, the reason for privileging Christianity from these parts of the world becomes an expressly political one. In other words, the quality or acceptability of one’s Christianity becomes dependent on the extent to which it complements the political values of modern Western states. Tying the importance of Christianity to the instrumental claim that Christianity is necessary because it created or undergirded our political culture takes us closer to defending Christianity in terms of little more than “Christian-flavored civic religion.” Even if it were true, I’m not sure that Christians should want to make that argument.
The American Radical Reformation tradition of evangelical Protestant Christianity is particularly prone to making really extreme conflations between Christianity and a specific concrete temporal order (or, at the other extreme reject the temporal order altogether as illegitimate) . I think it has to do with the sectarian and often parochial nature of American evangelical pastors, as opposed to more internationalist Roman Catholic clerics. This tendency is not necessarily good, or bad, as such. But it does lead to strange assertions of necessary entailments from Christian religious affiliation which would render most pre-modern Christians imperfectly Christian, and many non-Western Christians imperfectly Christian today (the attempts by American Protestants to convert Oriental Orthodox Christians in the Near East, traditions with a 2,000 year history, is a practical outcome of this mode of thinking). The Mormon church explicitly interjects Americocentrism into their religious system, taking these tendencies to their logical extreme, and arguably out of mainstream Christianity.
Interestingly, this way of thinking is not limited to Christians. I have observed American Muslims state that the United States is the most Islamic nation, the nation where Islam is practiced most freely and in its truest, pure, form. There were similar strands in 19th century Reform Judaism, which saw in America a nation where the Jewish religion could flourish without the impediments and historical baggage which had characterized Judaism in Europe, and so ushering in the Messianic era.
The common thread then is Americanism, not any particular religion.