I am posting simply Bible passages here, walking through the Biblical argument with minimal commentary or exposition. I’ll let the text speak for itself, and comment only to point out and emphasize things in the text. These are not the only supporting texts, nor is this post exhaustive.
The Covenant begins with Abraham. Circumcision as a covenant sign begins here with the Abrahamic covenant, not with the Mosaic administration:
When Abram was ninety-nine years old the Lord appeared to Abram and said to him, “I am God Almighty; walk before me, and be blameless, that I may make my covenant between me and you, and may multiply you greatly.” Then Abram fell on his face. And God said to him, “Behold, my covenant is with you, and you shall be the father of a multitude of nations. No longer shall your name be called Abram, but your name shall be Abraham, for I have made you the father of a multitude of nations. I will make you exceedingly fruitful, and I will make you into nations, and kings shall come from you. And I will establish my covenant between me and you and your offspring after you throughout their generations for an everlasting covenant, to be God to you and to your offspring after you. And I will give to you and to your offspring after you the land of your sojournings, all the land of Canaan, for an everlasting possession, and I will be their God.”
And God said to Abraham, “As for you, you shall keep my covenant, you and your offspring after you throughout their generations. This is my covenant, which you shall keep, between me and you and your offspring after you: Every male among you shall be circumcised. You shall be circumcised in the flesh of your foreskins, and it shall be a sign of the covenant between me and you. He who is eight days old among you shall be circumcised. Every male throughout your generations, whether born in your house or bought with your money from any foreigner who is not of your offspring, both he who is born in your house and he who is bought with your money, shall surely be circumcised. So shall my covenant be in your flesh an everlasting covenant. Any uncircumcised male who is not circumcised in the flesh of his foreskin shall be cut off from his people; he has broken my covenant.”
It is called an “everlasting covenant.” Hence, even with the end of the Mosaic administration, the Abrahamic covenant does not end there. This is also evidenced by other passages, which I’ll get to. But just keep in mind that circumcision is properly a feature of the Abrahamic covenant, not the Sinaitic.
Circumcision of the heart is not a concept exclusive to the New Covenant, but was commanded and anticipated in the Old Covenant from the very beginning:
Yet the Lord set his heart in love on your fathers and chose their offspring after them, you above all peoples, as you are this day. Circumcise therefore the foreskin of your heart, and be no longer stubborn.
And the LORD your God will circumcise your heart and the heart of your offspring, so that you will love the LORD your God with all your heart and with all your soul, that you may live.
Circumcise yourselves to the LORD; remove the foreskin of your hearts, O men of Judah and inhabitants of Jerusalem; lest my wrath go forth like fire, and burn with none to quench it, because of the evil of your deeds.”
“Behold, the days are coming, declares the Lord, when I will punish all those who are circumcised merely in the flesh— Egypt, Judah, Edom, the sons of Ammon, Moab, and all who dwell in the desert who cut the corners of their hair, for all these nations are uncircumcised, and all the house of Israel are uncircumcised in heart.”
Note that when Deuteronomy 30:6 speaks of circumcising hearts, it specifically mentions children. Offspring are put together with the adults to whom the promise is given. Keep this in mind for later as well.
Rather than lapsing into obsolescence, the Abrahamic covenant continues on and is fulfilled in Christ, and in all believers through Christ:
Galatians 3:7-9, 16-18, 25-29
Know then that it is those of faith who are the sons of Abraham. And the Scripture, foreseeing that God would justify the Gentiles by faith, preached the gospel beforehand to Abraham, saying, “In you shall all the nations be blessed.” So then, those who are of faith are blessed along with Abraham, the man of faith.
Now the promises were made to Abraham and to his offspring. It does not say, “And to offsprings,” referring to many, but referring to one, “And to your offspring,” who is Christ. This is what I mean: the law, which came 430 years afterward, does not annul a covenant previously ratified by God, so as to make the promise void. For if the inheritance comes by the law, it no longer comes by promise; but God gave it to Abraham by a promise.
But now that faith has come, we are no longer under a guardian, for in Christ Jesus you are all sons of God, through faith. For as many of you as were baptized into Christ have put on Christ. There is neither Jew nor Greek, there is neither slave nor free, there is no male and female, for you are all one in Christ Jesus. And if you are Christ’s, then you are Abraham’s offspring, heirs according to promise.
As God promised Abraham, all nations are blessed through him. The promise finds its fulfillment with the inclusion of the Gentiles into the covenant:
Ephesians 2:11-13, 19-21
Therefore remember that at one time you Gentiles in the flesh, called “the uncircumcision” by what is called the circumcision, which is made in the flesh by hands—remember that you were at that time separated from Christ, alienated from the commonwealth of Israel and strangers to the covenants of promise, having no hope and without God in the world. But now in Christ Jesus you who once were far off have been brought near by the blood of Christ.
So then you are no longer strangers and aliens, but you are fellow citizens with the saints and members of the household of God, built on the foundation of the apostles and prophets, Christ Jesus himself being the cornerstone, in whom the whole structure, being joined together, grows into a holy temple in the Lord.
Just as circumcision was for the infants of the covenant for Abraham, children are not excluded from the covenant with the coming of the New.
For the promise is for you and for your children and for all who are far off, everyone whom the Lord our God calls to himself.
The bloody sign of circumcision is no longer. But there still remains a covenant sign that corresponds to circumcision. And remember that circumcision of the heart was promised specifically for offspring in Deuteronomy 30:6:
In him also you were circumcised with a circumcision made without hands, by putting off the body of the flesh, by the circumcision of Christ, having been buried with him in baptism, in which you were also raised with him through faith in the powerful working of God, who raised him from the dead.
The apostles, in keeping with this covenant, baptized whole households with no qualification given:
Acts 16:14-15, 30-34
One who heard us was a woman named Lydia, from the city of Thyatira, a seller of purple goods, who was a worshiper of God. The Lord opened her heart to pay attention to what was said by Paul. And after she was baptized, and her household as well, she urged us, saying, “If you have judged me to be faithful to the Lord, come to my house and stay.” And she prevailed upon us.
Then he brought them out and said, “Sirs, what must I do to be saved?” And they said, “Believe in the Lord Jesus, and you will be saved, you and your household.” And they spoke the word of the Lord to him and to all who were in his house. And he took them the same hour of the night and washed their wounds; and he was baptized at once, he and all his family. Then he brought them up into his house and set food before them. And he rejoiced along with his entire household that he had believed in God.
Jesus uses the example of an infant as the state in which one must come to him to enter the kingdom. The kingdom is for infants and of them:
Now they were bringing even infants to him that he might touch them. And when the disciples saw it, they rebuked them. But Jesus called them to him, saying, “Let the children come to me, and do not hinder them, for to such belongs the kingdom of God. Truly, I say to you, whoever does not receive the kingdom of God like a child shall not enter it.”
Finally, Paul assumes the holiness of the children of believers when he argues for the sanctification of an unbelieving spouse by a believing one:
1 Corinthians 7:14
For the unbelieving husband is made holy because of his wife, and the unbelieving wife is made holy because of her husband. Otherwise your children would be unclean, but as it is, they are holy.