“as far as I know, the Ten Commandments apply to both Jews and Christians.”
Perhaps this is where you go wrong. The ten commandments do not apply to non-Jewish people, and never have.
The Laws of Noah (which are very similar) apply to non-Jewish people.
It’s a fundamental theological error.
Well, when I underwent Christian training as a youth, we were taught “The Ten Commandments” word-by-parsed-word, and had to memorize the commandment and the interpreted meaning.
We read that Moses brought the Ten Commandments, which were written by the hand of God, down from Mount Sinai, and upon seeing the sinful ways of the people....he smashed them in anger.
We were taught that the Old Testament was “The Law” and the New Testament was “The Gospel”.
I don’t know if God meant for gentiles to follow the Ten Commandments, but it seems (although it’s impossible to live without sin) that Conservative Christians try to live by them.
This is what I believed “Judeao-Christian” principles meant.
The Laws of Noah? Never heard of them.