Gentile believers are not living according to the Law of Moses. We are living according to grace and truth that comes by Jesus Christ. Gentiles have never had to convert to Judaism to be saved.
John 1:17 (KJV) For the law was given by Moses, but grace and truth came by Jesus Christ.
Gentiles are required to repent from their sins in accordance with the Gospel message and the Law of Moses was given to give us knowledge of what sin is (Romans 3:20).
There is no "but" in the Greek in John 1:17, rather 1:16 says grace upon grace, so it is using a parallel statement to talk about one example of grace and truth being added on top of other. In Psalms 119:29, David wanted God to be gracious to him by teaching him to obey the Mosaic Law, and in Psalms 119:142, the Mosaic Law is truth, which is the same grace and truth came through Jesus. Jesus spent his ministry teaching how to practice Judaism by living in sinless obedience to the Mosaic Law, so Gentiles can look at what he taught to practice and decide whether or not to follow him, but Gentiles can't follow him by refusing to follow what he taught. Our salvation is from sin (Matthew 1:21) and sin is the transgression of the Mosaic Law (1 John 3:4), so Jesus leading us to live in obedience to it is intrinsically the content of the gift of him saving us from not living in obedience to it, and it is contradictory for someone think that they they need salvation from sin while also thinking that they don't need to obey the Mosaic Law.
Now we know that what things soever the law saith, it saith to them who are under the law: that every mouth may be stopped, and all the world may become guilty before God. 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. But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets; Even the righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: for there is no difference: For all have sinned, and come short of the glory of God; Being justified freely by his grace through the redemption that is in Christ Jesus: Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God; To declare, I say, at this time his righteousness: that he might be just, and the justifier of him which believeth in Jesus. Where is boasting then? It is excluded. By what law? of works? Nay: but by the law of faith. Therefore we conclude that a man is justified by faith without the deeds of the law.
In Psalms 119:29-30, David wanted to put false ways far from him, for God to be gracious to him by teaching him to obey the Mosaic Law, and he chose the way of faithfulness, so this has always been the one and only way of salvation by grace through faith that is testified about in the Law and the Prophets. In Genesis 6:8-9, Noah found grace in the eyes of God, he was a righteous man, and he walked with God, so God was gracious to him by teaching him to obey His law, and he was righteous because he obeyed through faith, which is in the same manner as Abraham (Genesis 15:6) and everyone else.
In Romans 3:27, Paul contrasted a law of works with a law of faith, so works of the law are of works, while he said in Romans 3:31 that our faith does not abolish our need to obey the Mosaic Law, but rather our faith upholds it, so it is of faith.
Owe no man any thing, but to love one another: for he that loveth another hath fulfilled the law. For this, Thou shalt not commit adultery, Thou shalt not kill, Thou shalt not steal, Thou shalt not bear false witness, Thou shalt not covet; and if there be any other commandment, it is briefly comprehended in this saying, namely, Thou shalt love thy neighbour as thyself.
Love fulfills the Mosaic Law because everything in it is an example of what it means to correctly love God and our neighbor, which is why they all hang on the greatest two commandments, so they are all connected. For example, if someone's understand of loving our neighbor is not inclusive of the command to help the poor, then they would have an incomplete understanding of what is means to love our neighbor, and the same is true of God's other laws.
But what law does our faith uphold? Not the Old Covenant Mosaic Law, but the Law of faith that comes by grace.
In Exodus 33:13, Moses wanted God to be gracious to him by teaching him His way that he might know Him, in 1 Kings 2:1-3, God taught how to walk in His way through the Mosaic Law, and in John 17:3, knowing God and Jesus is eternal life, which is again the one and only way of salvation by grace through faith. There are many verses that connect our faith in God with our obedience to His law, such as in Matthew 23:23, Jesus said that faith is one of the weightier matters of the Mosaic Law. In James 2:18, he would show his faith by his works. In Revelation 14:12, those who kept faith in Jesus are the same as those who kept God's commandments. In Hebrews 3:18-19, disobedience to the Mosaic Law is equated with unbelief. In Numbers 5:6, disobedience to the Mosaic Law is described as breaking faith, so it is the law of faith that comes by grace.
Where is boasting then? It is excluded. By what law? of works? Nay: but by the law of faith. Therefore we conclude that a man is justified by faith without the deeds of the law. Is he the God of the Jews only? is he not also of the Gentiles? Yes, of the Gentiles also: Seeing it is one God, which shall justify the circumcision by faith, and uncircumcision through faith.
Both by faith, and through faith IOW faith is the instrumental cause of justification before God. The Jews keeping the Law by faith, believing the Law and Prophets that speak of the Messiah/Savior Who was to come. Gentiles through faith, believing the Gospel in the same way Abraham did and became the father of the faithful.
Galatians 3:8-10 (KJV) And the scripture, foreseeing that God would justify the heathen through faith, preached before the gospel unto Abraham, saying, In thee shall all nations be blessed. So then they which be of faith are blessed with faithful Abraham. For as many as are of the works of the law are under the curse: for it is written, Cursed is every one that continueth not in all things which are written in the book of the law to do them.
In Matthew 4:15-23, Jesus began his ministry with the Gospel message to repent for the Kingdom of God is at hand, which was a light to the Gentiles, and the Mosaic Law was how his audience knew what sin is, so repenting from our disobedience to it is an integral part of the Gospel message, which he prophesied would be proclaimed to all nations (Matthew 24:12-14), and which was the Gospel that was made known in advance to Abraham in accordance with the promise (Genesis 12:1-5). In Mosaic Law his how the children of Abraham knw how to live blessed lives by walking in God's way (Psalms 119:1-3), so the way to fulfill the promise of being a blessing to the nations is by teaching the nations to repent and obey it in accordance with the Gospel.
In Galatians 3:10-12, the Book of the Law curses those who do not rely on it, so those who instead rely on works of the law thereby come under the curse for not relying on the Book of the Law. Furthermore, Paul associated a quote from Habakkuk 2:4 saying that the righteous shall live by faith with a quote from Leviticus 18:5, where the one who obeys the Mosaic Law will attain life by it, so the righteous living by faith does not refer to a manner of living that is not in obedience to it. God is trustworthy, therefore His law is also trustworthy (Psalms 19:7), so to obediently rely on the Mosaic Law that God has instructed is to rely on God.
It's not "those who say that the Mosaic Law is not made for a righteous person". It is the Scriptures that say this.
While I agree that it says that the Mosaic Law is not made for a righteous person, you are the one who is trying to use that to justify doing what is unrighteous in disobedience to it, and are thereby becoming someone that it is for according to that verse. Instructions for how to live righteously are not made for those who are already living righteously, but rather they are needed to teach those who are not living righteously. It is absurd to think that once a unrighteous person becomes righteous that they are now free to go back to living unrighteously and then become an unrighteous person that the law is for again.
Why do you keep trying to force the Old Covenant Mosaic Law into the New Covenant in Christ? Christ came to fulfill the requirements of the Old Law. He did this by His cross, resurrection, and ascension. The Old is abolished in Christ.
In Jeremiah 31:33, the New Covenant involves God putting the Mosaic Law in our minds and writing it on our hearts, so that is the law of the New Covenant, which Christ spent his ministry fulfilling by teaching us how to walk in obedience to it by word and by example. Furthermore, in 1 John 2:6, those who are in Christ are obligated to walk in the same way he walked. In Matthew 5:17-19, Jesus said that he came not to abolish the Mosaic Law, but to fulfill it, so he did not abolish it. In Titus 2:14, Jesus gave himself to redeem us from all lawlessness and to purify for himself a people of his own possession who are zealous for doing good works, so becoming zealous for doing good works in obedience to the Mosaic Law is the way to believe in what Jesus accomplished through the cross, while returning to the lawlessness that he gave himself to redeem us from is the way to reject what he accomplished through the cross.
The Holy Ghost this signifying, that the way into the holiest of all was not yet made manifest, while as the first tabernacle was yet standing: Which was a figure for the time then present, in which were offered both gifts and sacrifices, that could not make him that did the service perfect, as pertaining to the conscience; Which stood only in meats and drinks, and divers washings, and carnal ordinances, imposed on them until the time of reformation. But Christ being come an high priest of good things to come, by a greater and more perfect tabernacle, not made with hands, that is to say, not of this building; Neither by the blood of goats and calves, but by his own blood he entered in once into the holy place, having obtained eternal redemption for us. For if the blood of bulls and of goats, and the ashes of an heifer sprinkling the unclean, sanctifieth to the purifying of the flesh: How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?
In Deuteronomy 30:15-20, obedience to the Mosaic Law brings life and a blessing while disobedience brings death and a curse, so choose life! Dead works are those that lead to death and curse, not those that lead to life and a blessing.
For the law having a shadow of good things to come, and not the very image of the things, can never with those sacrifices which they offered year by year continually make the comers thereunto perfect. For then would they not have ceased to be offered? because that the worshippers once purged should have had no more conscience of sins. But in those sacrifices there is a remembrance again made of sins every year. For it is not possible that the blood of bulls and of goats should take away sins. Wherefore when he cometh into the world, he saith, Sacrifice and offering thou wouldest not, but a body hast thou prepared me: In burnt offerings and sacrifices for sin thou hast had no pleasure.
The foreshadows testify about what is to come and we should live in a way that testifies about what is to come by obeying them rather than a way that denies the truth of what is to come.