I agree the Law of Moses is being discussed, but more precisely it is the abuse of the Law of Moses as a means of salvation that is the issue.
Acts 15:1 And certain men which came down from Judaea taught the brethren, and said, Except ye be circumcised after the manner of Moses, ye cannot be saved.
Acts 15:10 Now therefore why tempt ye God, to put a yoke upon the neck of the disciples, which neither our fathers nor we were able to bear?
Acts 15:11 But we believe that through the grace of the Master Yeshua Messiah we shall be saved, even as they.
The yoke of verse 10 is not the Law of Moses, but
trying to keep the Law to be saved which was an incredible burden they were unable to bear.
The word "For" in verse 21 means "for this reason" or "because". James only included four laws from the Law of Moses for Gentile converts to keep
because they would hear Moses read every
SABBATH and would eventually hear and learn the rest of the Law of Moses rather than having to keep everything all at once. Surely those four laws are not the only ones they ever need to keep. There are many laws far more important than those (Ten Commandments, etc). The fact is, those laws would allow for Jewish and Gentile converts to fellowship and break bread together more readily without the Jewish believers being totally revolted by Gentile practices.
In reality, James' judgment was to not give the Gentiles converts a choice, but to "tell them" what they must do. James was not telling them "the Law of Moses is abolished and now you are free to break any commandment you want".