The Bible itself does the same thing.
"In whom also ye are circumcised with the circumcision made without hands, in putting off the body of the sins of the flesh by the circumcision of Christ: Buried with him in baptism, wherein also ye are risen with [him] through the faith of the operation of God, who hath raised him from the dead. And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses" Col 2:11-13
Circumcision is the sign of incorporation into Abraham's descendants, into the people of the covenant. It is a sign of submission to the Law and a sign that prefigures that "circumcision of Christ", which is Baptism (cf. CCC #527).
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The chosen people received from God distinctive signs and symbols that marked its liturgical life. These are no longer solely celebrations of cosmic cycles and social gestures, but signs of the covenant, symbols of God's mighty deeds for His people. Among these liturgical signs from the Old Covenant are circumcision, anointing and consecrating of kings and priests, laying on of hands, sacrifices, and above all, the Passover. The Church sees in these signs a prefiguring of the sacraments of the New Covenant.
In His preacing, the Lord Jesus often makes use of signs of creation to make known the mysteries of God. He performs healings and illustrates His preaching with physical signs or symbolic gestures. He gives new meaning to the deeds and signs of the Old Covenant, above all, to the Exodus and the Passover, for He Himself is the meaning of these signs.
Since Pentecost, it is through the sacramental signs of His Church that the Holy Spirit carries on the work of sanctification. The sacraments of the Church do not abolish but purify and integrate all the richness of the signs and symbols of the cosmos and social life. Further, they fulfill the types and figures of the Old Covenant, signify and make actively present the salvation wrought by Christ, and prefigure and anticipate the glory of heaven.
(CCC # 1150-1152)
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In the Old Testament, God instituted an ordinance of circumcision as the normative way for bringing a male child into the Covenant (Gen 17:1-14) and this ritual symbolically stripped away the hardheartedness and obstinancy as well as symbolically showing one had entered into the covenant of God as part of His people:
And now, Israel, what doth the LORD thy God require of thee, but to fear the LORD thy God, to walk in all his ways, and to love him, and to serve the LORD thy God with all thy heart and with all thy soul, To keep the commandments of the LORD, and his statutes, which I command thee this day for thy good? Behold, the heaven and the heaven of heavens [is] the LORD'S thy God, the earth [also], with all that therein [is]. Only the LORD had a delight in thy fathers to love them, and he chose their seed after them, [even] you above all people, as [it is] this day. Circumcise therefore the foreskin of your heart, and be no more stiffnecked. For the LORD your God [is] God of gods, and Lord of lords, a great God, a mighty, and a terrible, which regardeth not persons, nor taketh reward: He doth execute the judgment of the fatherless and widow, and loveth the stranger, in giving him food and raiment. Love ye therefore the stranger: for ye were strangers in the land of Egypt. Thou shalt fear the LORD thy God; him shalt thou serve, and to him shalt thou cleave, and swear by his name. He [is] thy praise, and he [is] thy God, that hath done for thee these great and terrible things, which thine eyes have seen. Thy fathers went down into Egypt with threescore and ten persons; and now the LORD thy God hath made thee as the stars of heaven for multitude. Deut 10:12-22
And it shall come to pass, when all these things are come upon thee, the blessing and the curse, which I have set before thee, and thou shalt call [them] to mind among all the nations, whither the LORD thy God hath driven thee, And shalt return unto the LORD thy God, and shalt obey his voice according to all that I command thee this day, thou and thy children, with all thine heart, and with all thy soul; That then the LORD thy God will turn thy captivity, and have compassion upon thee, and will return and gather thee from all the nations, whither the LORD thy God hath scattered thee. If [any] of thine be driven out unto the outmost [parts] of heaven, from thence will the LORD thy God gather thee, and from thence will he fetch thee: And the LORD thy God will bring thee into the land which thy fathers possessed, and thou shalt possess it; and he will do thee good, and multiply thee above thy fathers. And the LORD thy God will circumcise thine heart, and the heart of thy seed, to love the LORD thy God with all thine heart, and with all thy soul, that thou mayest live. And the LORD thy God will put all these curses upon thine enemies, and on them that hate thee, which persecuted thee. And thou shalt return and obey the voice of the LORD, and do all his commandments which I command thee this day. And the LORD thy God will make thee plenteous in every work of thine hand, in the fruit of thy body, and in the fruit of thy cattle, and in the fruit of thy land, for good: for the LORD will again rejoice over thee for good, as he rejoiced over thy fathers: If thou shalt hearken unto the voice of the LORD thy God, to keep his commandments and his statutes which are written in this book of the law, [and] if thou turn unto the LORD thy God with all thine heart, and with all thy soul. Deut 30:1-10
For he is not a Jew, which is one outwardly; neither [is that] circumcision, which is outward in the flesh: But he [is] a Jew, which is one inwardly; and circumcision [is that] of the heart, in the spirit, [and] not in the letter; whose praise [is] not of men, but of God. Rom 2:28-29
And how does this "circumcision of the heart begin"?
Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death? Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life. For if we have been planted together in the likeness of his death, we shall be also [in the likeness] of [his] resurrection: Knowing this, that our old man is crucified with [him], that the body of sin might be destroyed, that henceforth we should not serve sin. Romans 6:3-6
Clearly, Scripture notes that the signs of the OT, in this case, circumcision, are replaced by the signs of the NT, Baptism. Both sacraments bring humans into the People of God. In both cases, the sign of the Covenant with God (and in both cases, parents on behalf of their children in many cases) begins one's life in God.
I am glad that you note that God's Work among His people continues, showing the continuity of His actions among the Jewish nation and then in the new dispensation, the universal Catholic Church... The OT was a shadow of the good things to come, pointing the way to the NT Covenant that Christ made with His people, those who believe in Him and obey His Word.
Regards
