“Judeo-Christian” is another false construct, not even as old as “the melting pot” or “a nation of immigrants”. From Wikipedia:
History of the term
The term is used, as “Judeo Christian”, at least as far back as in a letter from Alexander M’Caul dated October 17, 1821. The term in this case referred to Jewish converts to Christianity. The term is used similarly by Joseph Wolff in 1829, referring to a style of church that would keep with some Jewish traditions in order to convert Jews.
Use of the German term judenchristlich (“Jewish-Christian”), in a decidedly negative sense, can be found in the late writings of Friedrich Nietzsche, who emphasized what he saw as neglected aspects of continuity between the Jewish world view and that of Christianity. The expression appears in The Antichrist, published in 1895 and written several years earlier; a fuller development of Nietzsche’s argument can be found in a prior work, On the Genealogy of Morality.
Promoting the concept of United States as a Judeo-Christian nation first became a political program in the 1940s, in response to the growth of anti-Semitism in America. The rise of Nazi anti-semitism in the 1930s led concerned Protestants, Catholics, and Jews to take steps to increase understanding and tolerance.
In this effort, precursors of the National Conference of Christians and Jews created teams consisting of a priest, a rabbi, and a minister, to run programs across the country, and fashion a more pluralistic America, no longer defined as a Christian land, but “one nurtured by three ennobling traditions: Protestantism, Catholicism and Judaism….The phrase ‘Judeo-Christian’ entered the contemporary lexicon as the standard liberal term for the idea that Western values rest on a religious consensus that included Jews.”
Anyone who is using the term “Judeo-Christian” is referencing, consciously or not, left-wing anti-Christian agitprop. There are no historical “Judeo-Christian” values; to the extent there is overlap they are Christian values.
Note that “Judeo-Christian” in its post-1940s revisionist usage is a part of the same program as the 1965 Hart-Celler Act. It was adopted specifically to redefine America and destroy the historical fact of America having been founded as a de facto Christian nation.
It is also worth noting that despite Islam being related to both Christianity and Judaism in precisely the same manner, we do not hear much talk of “Judeo-Islam” or “Islamo-Christianity”, much less take seriously the idea that Americans must defer to Muslims or grant them any special status on those grounds.
To claim “Judeo-Christian” is nothing more than recognizing Christianity’s roots in the Old Testament is akin to claiming that “Communism” just means people sharing with other members of their community. Moreover, to claim that Christianity is “Judaic” in that sense is to erase the other tribes of Israel; it would be 12 times more accurate to say “Hebreo-Christian”, “Israeli-Christian” or “Jacobite-Christian”.