It's also a document that was, by its design, limited to orthodox Christians. That is, it's a document of consensus on political/moral issues among traditional Roman Catholics, evangelical Protestants, Anglicans, and capital O Orthodox Christians (in other words Nicene Christians).
Apparently, Chuck Colson informed Hugh Hewitt that the document was more than merely political or moral; it is theological. "Jews, Mormons, and others, were not invited to sign the document...because this is a specifically Christian statement, quoting from the Christian scriptures."
For historic orthodox purposes, the document seems undeniably "Christian." These signatories are likely folks who would agree with the proposition that you are not a "Christian" unless you endorse the Nicene orthodoxy that forms the lowest common denominator among them.
The definition of "Christianity" also reminds me of Dr. Gregg Frazer's 10 point historic definition for late 18th Century America, one that forms a lowest common denominator among the creeds of Christian Churches during said time period (though, there were no capital O Orthodox Christian Churches then and said Church denies original sin which is part of Frazer's 10 point test).
Yet Dr. Frazer's church minister and college President, Dr. John MacArthur, is one of a number of notable evangelicals who refuse to sign said document. I think Dr. Frazer has a similar personal view about Roman Catholics presenting a false gospel. That is, while Roman Catholics are certainly Christians for historic "orthodox" purposes, and even late 18th Century American purposes, to many evangelicals, for personal salvation purposes, they are not "Christians."
This is where the moral, meets the political, meets the historical, meets the personal. Yes, it's complicated.
It's interesting to see how even among those religious conservatives who agree on 1) Nicene orthodoxy, and 2) political-moral issues, their theology and the role it plays in their lives divides them in seemingly irreconcilable ways. See for instance, the comments section in this Uncommon Descent post on the topic.
Here is James White, another notable evangelical who refused to sign this declaration, on the un-ecumenical reasons evangelicals have for not singing this declaration:
There is no question that all believers need to think seriously about the issues raised by this declaration. But what is the only solution to these issues? Is the solution to be found in presenting a unified front that implicitly says "the gospel does not unite us, but that is not important enough to divide us"? I do not think so. What is the only power given to the church to change hearts and minds? United political power? Or the gospel that is trampled under foot by every Roman Catholic priest when he "re-presents" the sacrifice of Christ upon the Roman altar, pretending to be a priest, an "alter Christus"? Am I glad when a Roman clergyman calls abortion murder? Of course. But it exhibits a real confusion, and not a small amount of cowardice, it seems, to stop identifying the man's false gospel and false teaching simply because you are glad to have a few more on the "right" side of a vitally important social issue.
I note, based on my meticulous study of America's Founders and their religious beliefs, that whatever may divide the Christianity of Roman Catholics, evangelicals, and the Orthodox Church (i.e., the signatories of said declaration) they have far more in common with one another than they do with the "Protestant Christianity" of many key American Founders and the philosophers they followed (J. Adams, Jefferson, Franklin, probably Madison, Washington, and many others, and their key philosophical influences, Locke, Newton, Clarke, Milton, Priestley, Price, and Burgh).
Finally James White brings up an interesting point about Martin Luther King. Conservative Christians of the religious right have, of late, invoked his example as does this document. Dr. King certainly was religious, and presented his beliefs as "Christianity." However, under a doctrinal test that excludes Mormons, Jehovah's Witnesses as "Christians," it's not clear that Dr. King was a Christian. And it's also not clear that Dr. King, were he alive today, would have endorsed their views on political-moral issues either.
White reproduces the following from Dr. King on orthodox Christian doctrine:
The orthodox attempt to explain the divinity of Jesus in terms of an inherent metaphysical substance within him seems to me quite inadaquate. To say that the Christ, whose example of living we are bid to follow, is divine in an ontological sense is actually harmful and detrimental. To invest this Christ with such supernatural qualities makes the rejoinder: "Oh, well, he had a better chance for that kind of life than we can possible have." In other words, one could easily use this as a means to hide behind behind his failures. So that the orthodox view of the divinity of Christ is in my mind quite readily denied.
So why put forth King as explicitly Christian, but not invite the Jehovah's Witnesses, who would "quite readily deny" the deity of Christ as well? Perhaps a document that identifies Papal actions as explicitly Christian actions can be excused for its inherent self-contradiction.
As a non-Christian observer/scholar of these events, I note all of this for the sake of clarity. Before we move on, realize what we are dealing with.