The Roman Catholic Catechism spells out in no uncertain terms that circumcision under the Old Covenant is equivalent to baptism under the New Testament. You can see with your own eyes that is precisely how the Catholic catechism presents circumcision to baptism?
1150 Signs of the covenant. 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 consecration 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.
527 Jesus’ circumcision, on the eighth day after his birth,209 is the sign of his incorporation into Abraham’s descendants, into the people of the covenant. It is the sign of his submission to the Law 210 and his deputation to Israel’s worship, in which he will participate throughout his life. This sign prefigures that “circumcision of Christ” which is Baptism.21
CIRCUMCISION: The rite prescribed in Judaism and other cultures which involves cutting off the foreskin of a male. Circumcision was a sign of the covenant between God and his people Israel and prefigured the rite of Christian initiation in Baptism. Jesus was circumcised eight days after his birth in accord with Jewish law (527). - Glossary of the Catholic Catechism
The Catechism spells out in clear language that sacraments "communicates" spiritual life:
683 “No one can say ‘Jesus is Lord’ except by the Holy Spirit.”1 “God has sent the Spirit of his Son into our hearts, crying, ‘Abba! Father!’”2 This knowledge of faith is possible only in the Holy Spirit: to be in touch with Christ, we must first have been touched by the Holy Spirit. He comes to meet us and kindles faith in us. By virtue of our Baptism, the first sacrament of the faith, the Holy Spirit in the Church communicates to us, intimately and personally, the life that originates in the Father and is offered to us in the Son. Baptism gives us the grace of new birth in God the Father, through his Son, in the Holy Spirit. For those who bear God’s Spirit are led to the Word, that is, to the Son, and the Son presents them to the Father, and the Father confers incorruptibility on them. And it is impossible to see God’s Son without the Spirit, and no one can approach the Father without the Son, for the knowledge of the Father is the Son, and the knowledge of God’s Son is obtained through the Holy Spirit.3 684 Through his grace, the Holy Spirit is the first to awaken
1992 Justification has been merited for us by the Passion of Christ who offered himself on the cross as a living victim, holy and pleasing to God, and whose blood has become the instrument of atonement for the sins of all men. Justification is conferred in Baptism, the sacrament of faith. It conforms us to the righteousness of God, who makes us inwardly just by the power of his mercy. Its purpose is the glory of God and of Christ, and the gift of eternal life:40
CONCLUSION: Circumcision under the Old Covenant is sacramental like baptism under the New Covenant. That teach that Baptism "communicates" spiritual life. They teach that justification is communicated through baptism.
However, Paul's explanation of the relationship between justification and circumcision repudiates the Roman Catholic doctrine of sacraments.
According to Paul, the "blessing" of justification (imputed righteousness and forgiveness of sins) with was not received "in circumcision" but "in uncircumcision":
6 Even as David also describeth the blessedness of the man, unto whom God imputeth righteousness without works,
7 Saying, Blessed are they whose iniquities are forgiven, and whose sins are covered.
8 Blessed is the man to whom the Lord will not impute sin.
9 ¶ Cometh this blessedness then upon the circumcision only, or upon the uncircumcision also? for we say that faith was reckoned to Abraham for righteousness.
10 How was it then reckoned? when he was in circumcision, or in uncircumcision? Not in circumcision, but in uncircumcision.
Rome has acknowledged that circumcision under the old is equivalent to baptism under the New and so to test the Catholic view one merely can replace the term "circumcision" with "baptism" and you would have the consequences of Rome's view. So in the following text we replace "circumcision" and put in "baptism" as the Catechism of Rome claims to be equivilent with regard to sacramental value and this is what we end up with:
9 ¶ Cometh this blessedness then upon the BAPTIZED only, or upon the UNBAPTIZED also? For we say that faith was reckoned to Abraham for righteousness.
10 How was it then reckoned? when he was in BAPTISM, or UNBAPTIZED? Not in BAPTISM, butUNBAPTIZED.
11 And he received the sign of BAPTISM, a seal of the righteousness of the faith which he had yet being UNBAPTIZED: that he might be the father of all them that believe, though they be notBAPTIZED; that righteousness might be imputed unto them also:
12 And the father of BAPTISM to them who are not of the BAPTIZED only, but who also walk in the steps of that faith of our father Abraham, which he had being yet UNBAPTIZED.
As you can plainly see by placing "baptize" in the place of "circumcision" the whole Roman veiw of sacramental salvation is completely repudiated by Paul.
No doubt Catholics and Catholic sympathizers will not like this. They may attack the person who presents this. They may scorn it. However, it is clear that Paul did not believe that circumcision was a sacrament, nor "communicated" life or justifying grace. So the Catholic church has digged their own pit and fallen in it.
Moreover, redemptive language is commonly used for all Old Testament ceremonial ordinances and sacrifices. However, New Testament writers claim the ordinances and sacrifices themselves did not literally save or remit sins but did so only by type or like a "shadow" and never were able to remit sins literally (Heb. 10:1-4; Col. 2:14-16). Hence, the issue is not whether or not baptism and the Lord's Supper save for they do! But the issue is HOW do they save and the answer is FIGURATIVELY (1 Pet. 3:21; Rom. 4:11).
1150 Signs of the covenant. 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 consecration 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.
527 Jesus’ circumcision, on the eighth day after his birth,209 is the sign of his incorporation into Abraham’s descendants, into the people of the covenant. It is the sign of his submission to the Law 210 and his deputation to Israel’s worship, in which he will participate throughout his life. This sign prefigures that “circumcision of Christ” which is Baptism.21
CIRCUMCISION: The rite prescribed in Judaism and other cultures which involves cutting off the foreskin of a male. Circumcision was a sign of the covenant between God and his people Israel and prefigured the rite of Christian initiation in Baptism. Jesus was circumcised eight days after his birth in accord with Jewish law (527). - Glossary of the Catholic Catechism
The Catechism spells out in clear language that sacraments "communicates" spiritual life:
683 “No one can say ‘Jesus is Lord’ except by the Holy Spirit.”1 “God has sent the Spirit of his Son into our hearts, crying, ‘Abba! Father!’”2 This knowledge of faith is possible only in the Holy Spirit: to be in touch with Christ, we must first have been touched by the Holy Spirit. He comes to meet us and kindles faith in us. By virtue of our Baptism, the first sacrament of the faith, the Holy Spirit in the Church communicates to us, intimately and personally, the life that originates in the Father and is offered to us in the Son. Baptism gives us the grace of new birth in God the Father, through his Son, in the Holy Spirit. For those who bear God’s Spirit are led to the Word, that is, to the Son, and the Son presents them to the Father, and the Father confers incorruptibility on them. And it is impossible to see God’s Son without the Spirit, and no one can approach the Father without the Son, for the knowledge of the Father is the Son, and the knowledge of God’s Son is obtained through the Holy Spirit.3 684 Through his grace, the Holy Spirit is the first to awaken
1992 Justification has been merited for us by the Passion of Christ who offered himself on the cross as a living victim, holy and pleasing to God, and whose blood has become the instrument of atonement for the sins of all men. Justification is conferred in Baptism, the sacrament of faith. It conforms us to the righteousness of God, who makes us inwardly just by the power of his mercy. Its purpose is the glory of God and of Christ, and the gift of eternal life:40
CONCLUSION: Circumcision under the Old Covenant is sacramental like baptism under the New Covenant. That teach that Baptism "communicates" spiritual life. They teach that justification is communicated through baptism.
However, Paul's explanation of the relationship between justification and circumcision repudiates the Roman Catholic doctrine of sacraments.
According to Paul, the "blessing" of justification (imputed righteousness and forgiveness of sins) with was not received "in circumcision" but "in uncircumcision":
6 Even as David also describeth the blessedness of the man, unto whom God imputeth righteousness without works,
7 Saying, Blessed are they whose iniquities are forgiven, and whose sins are covered.
8 Blessed is the man to whom the Lord will not impute sin.
9 ¶ Cometh this blessedness then upon the circumcision only, or upon the uncircumcision also? for we say that faith was reckoned to Abraham for righteousness.
10 How was it then reckoned? when he was in circumcision, or in uncircumcision? Not in circumcision, but in uncircumcision.
Rome has acknowledged that circumcision under the old is equivalent to baptism under the New and so to test the Catholic view one merely can replace the term "circumcision" with "baptism" and you would have the consequences of Rome's view. So in the following text we replace "circumcision" and put in "baptism" as the Catechism of Rome claims to be equivilent with regard to sacramental value and this is what we end up with:
9 ¶ Cometh this blessedness then upon the BAPTIZED only, or upon the UNBAPTIZED also? For we say that faith was reckoned to Abraham for righteousness.
10 How was it then reckoned? when he was in BAPTISM, or UNBAPTIZED? Not in BAPTISM, butUNBAPTIZED.
11 And he received the sign of BAPTISM, a seal of the righteousness of the faith which he had yet being UNBAPTIZED: that he might be the father of all them that believe, though they be notBAPTIZED; that righteousness might be imputed unto them also:
12 And the father of BAPTISM to them who are not of the BAPTIZED only, but who also walk in the steps of that faith of our father Abraham, which he had being yet UNBAPTIZED.
As you can plainly see by placing "baptize" in the place of "circumcision" the whole Roman veiw of sacramental salvation is completely repudiated by Paul.
No doubt Catholics and Catholic sympathizers will not like this. They may attack the person who presents this. They may scorn it. However, it is clear that Paul did not believe that circumcision was a sacrament, nor "communicated" life or justifying grace. So the Catholic church has digged their own pit and fallen in it.
Moreover, redemptive language is commonly used for all Old Testament ceremonial ordinances and sacrifices. However, New Testament writers claim the ordinances and sacrifices themselves did not literally save or remit sins but did so only by type or like a "shadow" and never were able to remit sins literally (Heb. 10:1-4; Col. 2:14-16). Hence, the issue is not whether or not baptism and the Lord's Supper save for they do! But the issue is HOW do they save and the answer is FIGURATIVELY (1 Pet. 3:21; Rom. 4:11).