You refer to Jeremiah 31:31 as a proof text to prove that it is no longer necessary to keep the Sabbath. Have you noticed who the New Covenant is made with? It is with the House of Israel and the House of Judah. Paul cites this in Hebrew 8:8 also. If you don’t belong to either the House of Judah or the House of Israel, it is a moot point because the covenant isn’t made with anyone else. Hear me out now. There is no place in Scripture that says the Church replaces
"Behold, the days are coming, says the LORD, when I will make a new covenant with the house of Israel and with the house of Judah - not according to the covenant that I made with their fathers in the day that I took them by the hand to lead them out of the land of Egypt, My covenant which they broke, though I was a husband to them, says the LORD. But this is the covenant that I will make with the house of Israel after those days, says the LORD: I will put My law in their minds, and write it on their hearts; and I will be their God, and they shall be My people. No more shall every man teach his neighbor, and every man his brother, saying, 'Know the LORD,' for they all shall know Me, from the least of them to the greatest of them, says the LORD. For I will forgive their iniquity, and their sin I will remember no more" (Jeremiah 31:31-34).
Just as the new covenant saved the Gentiles, it save Israel as well because they too were invited to join it. But the Gentiles were not required to become Israelites to enter into that new covenant. Quite the opposite; the Israelites had to leave the old covenant to be joined to the new. "Or do you not know, brethren (for I speak to those who know the law), that the law has dominion over a man as long as he lives? For the woman who has a husband is bound by the law to her husband as long as he lives. But if the husband dies, she is released from the law of her husband. So then if, while her husband lives, she marries another man, she will be called an adulteress; but if her husband dies, she is free from that law, so that she is no adulteress, though she has married another man. Therefore, my brethren, you also have become dead to the law through the body of Christ, that you may be married to another--to Him who was raised from the dead, that we should bear fruit to God. For when we were in the flesh, the sinful passions which were aroused by the law were at work in our members to bear fruit to death. But now we have been delivered from the law, having died to what we were held by, so that we should serve in the newness of the Spirit and not in the oldness of the letter" (Romans 7:1-6).
Thus in Christ's covenant there is no longer a distinction between Jews and Gentiles. "There is neither Jew nor Greek, there is neither slave nor free, there is neither male nor female; for you are all one in Christ Jesus" (Galatians 3:28). "For He Himself is our peace, who has made both one, and has broken down the middle wall of separation, having abolished in His flesh the enmity, that is, the law of commandments contained in ordinances, so as to create in Himself one new man from the two, thus making peace, and that He might reconcile them both to God in one body through the cross, thereby putting to death the enmity" (Ephesians 2:14-16). "And you, being dead in your trespasses and the uncircumcision of your flesh, He has made alive together with Him, having forgiven you all trespasses, having wiped out the handwriting of requirements that was against us, which was contrary to us. And He has taken it out of the way, having nailed it to the cross" (Colossians 2:13-14).
The witness to the Old Covenant with Israel was circumcision. An uncircumcised man was excluded from Israel because he had not accepted the covenant. Yet under Christ's law Paul taught, "Stand fast therefore in the liberty by which Christ has made us free, and do not be entangled again with a yoke of bondage. Indeed I, Paul, say to you that if you become circumcised, Christ will profit you nothing. And I testify again to every man who becomes circumcised that he is a debtor to keep the whole law. You have become estranged from Christ, you who attempt to be justified by law; you have fallen from grace" (Galatians 5:1-4).
Now what did Paul teach about Israel in Romans 11? "For I speak to you Gentiles; inasmuch as I am an apostle to the Gentiles, I magnify my ministry, if by any means I may provoke to jealousy those who are my flesh and save some of them. For if their being cast away is the reconciling of the world, what will their acceptance be but life from the dead? For if the firstfruit is holy, the lump is also holy; and if the root is holy, so are the branches. And if some of the branches were broken off, and you, being a wild olive tree, were grafted in among them, and with them became a partaker of the root and fatness of the olive tree, do not boast against the branches. But if you do boast, remember that you do not support the root, but the root supports you. You will say then, "Branches were broken off that I might be grafted in." Well said. Because of unbelief they were broken off, and you stand by faith. Do not be haughty, but fear. For if God did not spare the natural branches, He may not spare you either. Therefore consider the goodness and severity of God: on those who fell, severity; but toward you, goodness, if you continue in His goodness. Otherwise you also will be cut off" (Romans 11:13-22). Notice that in this passage Paul states that Israel, repesented as the natural branches, were broken off because of their unbelief. This allowed God to graft in the Gentiles, represented as the wild olive tree branches. In your contention you assume that the base tree is Israel, but that is not what Paul stated. It cannot be so because Israel was broken off.
In regards to the relationship of Israel and the church:
"For he is not a Jew who is one outwardly, nor is circumcision that which is outward in the flesh; but he is a Jew who is one inwardly; and circumcision is that of the heart, in the Spirit, not in the letter; whose praise is not from men but from God" (Romans 2:28-29).
"And he received the sign of circumcision, a seal of the righteousness of the faith which he had while still uncircumcised, that he might be the father of all those who believe, though they are uncircumcised, that righteousness might be imputed to them also, and the father of circumcision to those who not only are of the circumcision, but who also walk in the steps of the faith which our father Abraham had while still uncircumcised. For the promise that he would be the heir of the world was not to Abraham or to his seed through the law, but through the righteousness of faith. For if those who are of the law are heirs, faith is made void and the promise made of no effect, because the law brings about wrath; for where there is no law there is no transgression. Therefore it is of faith that it might be according to grace, so that the promise might be sure to all the seed, not only to those who are of the law, but also to those who are of the faith of Abraham, who is the father of us all" (Romans 4:11-16).
"But it is not that the word of God has taken no effect. For they are not all Israel who are of Israel, nor are they all children because they are the seed of Abraham; but, "In Isaac your seed shall be called." That is, those who are the children of the flesh, these are not the children of God; but the children of the promise are counted as the seed" (Romans 9:6-8).
Under the new covenant a physical relationship no longer determined who were God's people. God's people, spiritual Israel if you would, is composed of those who believe. They were not required to become a part of physical Israel because that age had past. Nor are those of the new covenant required to bind themselves under the old covenant. "He takes away the first that He may establish the second" (Hebrews 10:9). "In that He says, "A new covenant," He has made the first obsolete. Now what is becoming obsolete and growing old is ready to vanish away" (Hebrews 8:13).