What differences do you attribute to "Judeo-Christian morality" in contrast to "Christian morality"?
That is an extremely important question and it deserves pages, not paragraphs.
The short version is that I see the American Constitution as being founded on more broadly Judeo-Christian values, not an explicitly Christian society. That has many consequences in both theory and practice. For example, there are major differences between the original intent of the United States Constitution and the original intent of the Puritan founders of New England.
I could say a great deal more but I'm not sure if I'd be answering your question or going in a side track. The short answer is that I am very glad that the United States is a nation where basic principles of Judeo-Christian morality have historically been honored without establishing a formal state church. The result is Roman Catholics, Jewish people, and a wide variety of Protestant denominations have been able to live in relative peace compared to what was happening in Europe with its formally established state churches.
I have some very strongly conservative theological positions which look much more like Puritan New England than like the principles adopted at the Constitutional Convention, but by the late 1700s there was no realistic way to follow that earlier model on a national level. While that certainly had some negative consequences, among the greatest benefits is that the United States became a place where Jewish people could worship freely and be considered good American citizens.
Again, more could be said but I don't want to get off track by answering questions you may not have intended to ask.