The Rambam in Hilchos Melachim 8:10-11 (see also Likkutei Sichos vol. 26 p. 132) rules it is a prerequisite of the 7 Noahide Laws that Gentiles bide by them because it says so in “the Torah of Moses".
"Anyone who accepts upon himself and carefully observes the Seven Commandments is of the Righteous of the Nations of the World and has a portion in the World to Come. This is as long as he accepts and performs them because (he truly believes that) it was the Holy One, Blessed Be He, Who commanded them in the Torah, and that it was through Moses our Teacher that we were informed that the Sons of Noah had already been commanded to observe them. But if he observes them because he convinced himself logically, then he is not considered a Resident Convert and is not of the Righteous of the Nations of the World, but merely one of their wise."
Accordingly, does the Christian doctrine of the abrogation of the “Old Testament” by the “New Testament” of Yoshke, disqualify adherents of Christianity as Pious Amongst the Nations.
(Provided they don’t believe in the trinity nor consider Yoshke an incarnation of G-d ח״ו, otherwise they are oivdei avodah zarah mamash not shituf as per psak of HaRav Moshe Sternbuch ראב״ד of the Edah HaChareidis)