On what basis do Protestants extend the New Covenant to include gentiles? Given &quot;sola scriptura&quot; and the explicit assertions in scripture regarding the participants in the covenant (&quot;the houses of Israel and Judah&quot;) how do Protestants justify teaching it to be for gentile Protestants?

Jer 31:31 KJV - 31 Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah:
Heb 8:8 KJV - 8 For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah:

Isn't this overreach that is contrary to sola scriptura?
Update for clarification
I'm not concerned that the gospel only applies to Jews (gentiles do have &quot;access by faith into the grace&quot;) but rather the covenants:

Rom 9:4 ASV - 4 who are Israelites; whose is the adoption, and the glory, and the covenants, and the giving of the law, and the service of God, and the promises;

I'm seeking maybe a &quot;theodicy&quot; about gentiles and the new covenant from a representative &quot;Reformer&quot; and why, since they are all about &quot;sola fida&quot; and &quot;sola scriptura&quot; do they commandeer the explicitly Jewish new covenant as well?
1. The New Covenant is the Gospel of the Cross

Luke 22:19-20: And he took bread, and when he had given thanks, he broke it and gave it to them, saying, “This is my body, which is given for you. Do this in remembrance of me.” And likewise the cup after they had eaten, saying, “This cup that is poured out for you is the new covenant in my blood.”

From these verses we can see that the Lord's Supper was instituted as a sign of the New Covenant, and the New Covenant is Jesus' giving of his own body and blood on the cross. The New Covenant is the Gospel: the good news of the forgiveness of sins and reconciliation to God through being united to Jesus in his death and resurrection. And as the New Testament clearly teaches in so many places that the Gospel is for all peoples, including Gentiles, so we know that Gentiles are included in the New Covenant. But the mechanisms by which Gentiles are included is a little less clear, so let's look at that now.
2. Adopted as Abraham's spiritual children
There is a lot of disagreement among Christians over the relationship between the Church and Israel, ranging from the Church completely replacing Israel, to the two existing in parallel with little to connect them. I won't try to give a full overview of this issue, instead I'll just focus on one chapter, Romans 4. In this chapter Paul highlights that Abraham was declared righteous before he was circumcised, meaning that faith is prior to law. The true heirs of Abraham are not his physical descendants, but his spiritual descendants, who share his faith. If this is true for the Abrahamic Covenant, then even more so for the New Covenant.

Romans 4:11-13: He received the sign of circumcision as a seal of the righteousness that he had by faith while he was still uncircumcised. The purpose was to make him the father of all who believe without being circumcised, so that righteousness would be counted to them as well, and to make him the father of the circumcised who are not merely circumcised but who also walk in the footsteps of the faith that our father Abraham had before he was circumcised. For the promise to Abraham and his offspring that he would be heir of the world did not come through the law but through the righteousness of faith.
Romans 4:16-17: That is why it depends on faith, in order that the promise may rest on grace and be guaranteed to all his offspring—not only to the adherent of the law but also to the one who shares the faith of Abraham, who is the father of us all, as it is written, “I have made you the father of many nations”—in the presence of the God in whom he believed, who gives life to the dead and calls into existence the things that do not exist.

3. United with Christ in his death
A third way in which we can understand Gentiles being part of the New Covenant is our doctrine of Union with Christ. More than any other covenant, the New Covenant is the covenant of Jesus Christ. We are united to him in his death and resurrection, so the life of the Christian is the life of Jesus. As Jesus was in every sense a Jew, both spiritually and biologically, the Gentiles who live in Jesus share his Jewish life and participation in the New Covenant.

Romans 6:1-11: What shall we say then? Are we to continue in sin that grace may abound? By no means! How can we who died to sin still live in it? Do you not know that all of us who have been baptized into Christ Jesus were baptized into his death? We were buried therefore with him by baptism into death, in order that, just as Christ was raised from the dead by the glory of the Father, we too might walk in newness of life. For if we have been united with him in a death like his, we shall certainly be united with him in a resurrection like his. We know that our old self was crucified with him in order that the body of sin might be brought to nothing, so that we would no longer be enslaved to sin. For one who has died has been set free from sin. Now if we have died with Christ, we believe that we will also live with him. We know that Christ, being raised from the dead, will never die again; death no longer has dominion over him. For the death he died he died to sin, once for all, but the life he lives he lives to God. So you also must consider yourselves dead to sin and alive to God in Christ Jesus.