The Jerusalem Council in Acts 15 makes it clear that there are only four requirements of Gentile Christians:
Therefore it is my judgment that we do not trouble those who are turning to God from among the Gentiles, but that we write to them that they abstain from things contaminated by idols and from fornication and from what is strangled and from blood. (Acts 15:19-20)
Clearly the Law of Moses does not apply to us!
A quick check of the beginning of the chapter makes it clear that the context of this passage is focused on the question of whether or not works (specifically circumcision) are required for salvation:
Some men came down from Judea and began teaching the brethren, "Unless you are circumcised according to the custom of Moses, you cannot be saved." (Acts 15:1)
The whole of Scripture is clear: salvation is by faith... not works. Works come afterwards as a result of salvation.
The suggestion that Gentile Christians are only given these four requirements is ill conceived. Did the Jerusalem council intend to permit Gentile believers to commit theft, coveting, blasphemy, and every sin other than the four items specifically prohibited in verse 20?
Not at all!
These were simply the first, clear cut social conditions required to allow Gentile believers into fellowship with what was (at that time) an entirely Jewish assembly of believers.
The remainder of James' statement is enlightening:
"Therefore it is my judgment that we do not trouble those who are turning to God from among the Gentiles, but that we write to them that they abstain from things contaminated by idols and from fornication and from what is strangled and from blood. For Moses from ancient generations has in every city those who preach him, since he is read in the synagogues every Sabbath." (Acts 15:19-21)
Was James implying that Gentiles would come to learn the commandments because they would be assembling with the Jewish believers every week in the synagogue?
It's something to consider.