(NOTE: I did not study NCT because I wanted to be an adherent; I searched the Scriptures and discovered that my view had major similarities with what NCT teaches.)
NCT adherents do not keep a Sabbath day, ie, remembering the Sabbath day to keep it holy is not in their list of what God desires of them as Christians.
The argument re: the Sabbath becomes passe if you consider that the Ten Commandments was intended only for the Jews. Subsequent reiterations of and indictments about not keeping Sabbaths in the Prophets are clearly against the Jews only.
A singular example in the time of Nehemiah (Ch.13) makes this evident. At the time, merchants from Tyre came to the city (Jerusalem) and sold “fish and all manner of ware on the Sabbath” (v.16) to the children of Judah. Nehemiah rebuked them. He rebuked both “the nobles of Judah” (v.17) and “the merchants and sellers” (vv.20, 21.) His rebuke showed a clear understanding of the nature of the Sabbath command.
First he said to the nobles of Judah, “Why do you profane the Sabbath day? Did not your fathers thus, and did not our God bring all this evil upon us, and upon this city? yet ye bring more wrath upon Israel by profaning the Sabbath!” (vv.17, 18.)
Then, later, he said to the merchants and sellers, waiting for the city gates to open so they can sell on the Sabbath “Why lodge ye about the wall, if ye do so again, I will lay hands on you!” (v.21.) These merchants and sellers were obviously not under the Sabbath as the Jews were.
There is a far more important reason why I don’t believe in keeping Sabbaths. Sabbath keeping was never taught in the NT. Nowhere in the NT — in Acts and especially in the epistles to the churches — is there any reference to, examples of, or instructions on Sabbath keeping for the church to follow. None at all. Thus, neither is there any warning or rebuke towards Christians breaking or profaning the Sabbath.
There is, however, sufficient evidence to support the notion that the church, as a practice, gathered and met on the first day of the week. It appears to have been made the initial pattern set by the apostles. However, to say that this gathering of Christians on the first day of the week was according to the 4th commandment is a far stretch of the imagination the Apostles obviously never actually taught. The Christians’ gathering on the first day of the week was entirely different from the Jewish Sabbath which was still widely observed by the Jews at the time.