There you are contrasting values vs. society.
My question, rather, is how do you contrast "Judeo-Christian" vs. "Christian', let's say "Judeo-Christian values" vs. "Christian values".
When I speak of “Christian values” I'm defining that by the teachings of both the Old and New Testaments. To be slightly more specific, when I use that phrase in a secular governmental context, I would probably in most cases use that phrase intending to avoid getting into doctrinal issues between Protestantism and Roman Catholicism, and focusing on application of those values to society rather than in an ecclesiastical context.
When I speak of “Judeo-Christian values” in a secular governmental context, I typically use that term specifically to focus on the commonly-shared values of both the Jewish and Christian faiths. A short way of summarizing that would be to say that the Old Testament (or as Jewish people often prefer to say, the “Hebrew Bible”) teaches many things about how individuals, families and societies can govern themselves, and those are very good principles regardless of whether we profess the Jewish or Christian religions.
The Reformed tradition divides Old Testament laws into the three categories of moral, civil, and ceremonial law, with the moral law binding forever, the civil law useful in its “general equity” as an example for modern societies, and the ceremonial law (temple sacrifices, etc.) being fulfilled by the death of Christ. Obviously Jewish believers would disagree with that, and so would a fair number of modern evangelical Christians.
My point is not to focus on the details of the Westminster Confession of Faith, but rather to say that there is a common core of Judeo-Christian values which I think we can point to as a basis for a well-functioning American society. That common core of values does not require belief in Christ or some other doctrinal test to be a good American citizen, and that is part of what makes the American Constitution significantly different from the older principles of New England.
Am I answering your question or am I misunderstanding you?