The old covenant revealed sin. Paul wrote, "Therefore by the deeds of the law there shall no flesh be justified in his sight: for by the law is the knowledge of sin" (Romans 3:20).
A gentile or non-Jew was never included as part of the Old Testament. He was not subject unto its laws. The Jews (ie. descendants of Abraham and Sarah through Isaac and through Jacob) made up the priesthood and kingdom of Israel. The only way that a gentile could be a part of that covenant was to become a Jewish proselyte. The Old covenant was given by God to govern Israel as a nation and as a Kingdom. If the Old Testament was still in force, it would still apply to the Israelites only.
The old covenant went out of effect after the testator of the New Testament died. Hebrews 9:16 says, "For where a testament is, there must also of necessity be the death of the testator." The testator of the New Testament is Christ Jesus. Paul wrote, "Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross" (Colossians 2:14). Thus, the Old Testament went out of effect at the death of Jesus. The New Testament of the testator was made known at the first preaching of the gospel of Christ on the day of Pentecost in the city of Jerusalem as was prophesied.
The old covenant could not take away sins. Hebrews 10:4 & 11 says,
"For it is not possible that the blood of bulls and of goats should take away sins." (11) "And every priest standeth daily ministering and offering oftentimes the same sacrifices, which can never take away sins."
The old covenant was a shadow and not the real. Hebrews 8:5 says that the Old Testament priests "serve unto the example and shadow of heavenly things."
Since the Bible teaches these things concerning the Old Testament then we should not live according to the Ten Commandments or any other Old Testament mandate. To go back to the Old Testament is to go back to a time when sin could not be removed. Thus, "Christ is become of no effect unto you, whosoever of you are justified by the law; ye are fallen from grace" (Galatians 5:4). Since the law of Moses was a shadow and could not take away sins, why would anyone want to live under the Old Testament?