This is a tired argument and needs to be put to rest. The covenant was not made with all gentiles, period. Were there a few gentiles among the Israelites? Yes. Their presence is incidental, not material, to the covenant. Not until a gentile had submitted to all the requirements under the Law, were they considered "part of" Israel; mere belief was not sufficient.
Multitudes is not the same as a few and they were included into Israel, so you are hand waving. The Mosaic Law is the instructions of the God of Israel for how to believe in Him, which is why there are many verses that connect our faith or belief in God with our obedience to Him, such as Revelation 14:12, where those who kept faith in Jesus are the same as those who kept God's commandments. By doing good works in obedience to the Mosaic Law, we are testifying that God is good, which is why our good works bring glory to Him (Matthew 5:16), and by testifying that God is good, we are also expressing the belief that He is good, or in other words, we are believing in Him. In other words, the way to believe in God is by being conformed to His image, so the way to believe that God is righteous is by doing what ice righteous, the way to believe that God is holy is by being holy as He is holy, and so forth. So only those who obey the Mosaic Law believe in the God of Israel.
Your statement is awkward and is crying out for clarification, but I'll let it go for now.
The New Covenant was only made with the house of Judah and the house of Israel, so if a Gentiles wants to partake in the New Covenant, then they need to become part of Israel, which happens through faith in the God of Israel/Christ.
Um, no. It involves believing in Jesus Christ for salvation.
While it is true that the New Covenant involvers believing in Jesus Christ for salvation, that does not mean that it is false that according to Jeremiah 31:33, it involves God putting the Mosaic Law in our minds and writing it on our hearts, especially because the Mosaic Law is God's instructions for how to believe in Jesus Christ for salvation.
That doesn't make any sense.
In Exodus 33:13, Moses wanted God to be gracious to him by teaching him to walk in His way that he and Israel might know Him, and in 1 Kings 2:1-3, God taught how to walk in His way through the Mosaic Law, so if a Gentile wants to know the God of Israel, which is eternal life (John 17:3), then they need to follow the Mosaic Law, which is also why Jesus said that the way to inherit eternal life is by obeying God's commandments (Matthew 19:17, Luke 10:25-28).
The God of Israel also gave instructions to the Israelites for how to worship Him, so if a Gentile wants to worship the God of Israel, then they need to follow those instructions.
Likewise, the Bible repeatedly says in both the NT and the OT that if we love the God of Israel, then we will obey His commandments, so if someone wants to love God, then they need to obey His commandments, and it is impossible to love God instead of obeying His commandments. So by following instructions for the God of Israel for how to be holy as He is holy, we are knowing His holiness, we are loving His holiness, we are worshipping His holiness, we are believing in His holiness, and we are testifying about His holiness, so Gentiles who want to know, love, worship, believe, and testify about the God of Israel need to follow those instructions.
Again, that doesn't make sense. God didn't tell us to "follow Christ's example"; He told us to "believe in the One He has sent": Jesus. There is a massive difference. Jesus' ministry was primarily to people who were under the Sinai covenant, not the new covenant. Of course He taught them to follow Moses. However, upon His death, that covenant came to an end and the new covenant in His blood was initiated.
In Matthew 4:15-23, Christ began his ministry with the Gospel message to repent for the Kingdom of God is at hand, which was a light to the Gentles, and the Mosaic Law was how his audience knew what sin is (Romans 3:20), so repenting from our disobedience to it is a central part of the Gospel message. Furthermore, Christ set a sinless example of how to walk in obedience to the Mosaic Law and as his followers we are told to follow his example (1 Peter 2:21-22), that those who are in Christ are obligated to walk in the same way he walked (1 John 2:6), and to be imitators of Paul as he is of Christ (1 Corinthians 11:1). The fact that we are to believe in the one that God has sent does not mean that we are not instructed to follow his example, especially because following his example is the way to believe in the one that God has sent. Jesus did not establish the New Covenant for the purpose of undermining anything that he spent his ministry teaching by word or by example, but rather the New Covenant still involves following the Mosaic Law (Jeremiah 31:33). Moreover, John 12:46-50 does not give us any room to disregard anything that Jesus taught during his ministry. 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 his ministry and through the cross (Acts 21:20).