I believe Paul was addressing believers in Rome and not Jews in the second chapter. He is using the argument to prevent believers, particularly Jewish ones, from falling into the pitfalls of self-righteousness. I don't think he is so concerned with Jews as with Judiazers, those who would weaken or dismantle trust in Christ with the traditions and rules of Judaism.
In verses 25-29 Paul says:
Circumcision has value if you observe the law, but if you break the law, you have become as though you had not been circumcised. So then, if those who are not circumcised keep the law’s requirements, will they not be regarded as though they were circumcised? The one who is not circumcised physically and yet obeys the law will condemn you who, even though you have the written code and circumcision, are a lawbreaker.
A person is not a Jew who is one only outwardly, nor is circumcision merely outward and physical. No, a person is a Jew who is one inwardly; and circumcision is circumcision of the heart, by the Spirit, not by the written code. Such a person’s praise is not from other people, but from God.I like the contrasts Paul uses in 28-29 to talk about being a Jew inwardly versus being one outwardly. Three things mark a real Jew (and by extension, a real follower of God in Christ), circumcision of the heart, circumcision by the Spirit, and receiving praise from God. Paul explains circumcision for the believer even more clearly in Colossians 2:
In him you were also circumcised with a circumcision not performed by human hands. Your whole self ruled by the flesh was put off when you were circumcised by Christ, having been buried with him in baptism, in which you were also raised with him through your faith in the working of God, who raised him from the dead. (vv. 11-12)Circumcision is the putting off, the cutting off of the flesh in the life of the believer. This happens at through regeneration ("you were raised with him") which starts a process that continues throughout the life of a believer ("through your faith") as the old, dead part of their life is removed and replaced with a new, glorious life ("the working of God").
Roughly speaking, Christ's circumcision was performed in his death. The flesh was removed from him. He received a new body no longer affected by the flesh - mere temporary human effort and ability. The circumcised life is one lived without dependence on the flesh, but dependence on God. The fleshly life is cut away leaving a mark of God's work on that life.
This dependence on God, then is characterized by the three things above. First, it operates from the center of one's being rather than merely on the surface. The circumcision must cut deeply enough to bring about a change of heart rather than just a change of behavior. It works from the inside out.
Second, it is surrounded by things that cannot be explained with normal behavior or circumstances. Circumcision by the written code or letter is one of mere agreement and profession, but only brings obligation and shame. Such circumcision ends up cutting again and again, trying to make sure it is proved and real. Circumcision by the Spirit is a changed and changing life, operating with confidence and power evident through the work of the Spirit. It defies explanation and brings healing and a salvation without regret.
Third, this dependence on God runs on the affirmation from God himself over and against the approval or disapproval of people. Circumcision that brings the praise of people is based on behavior and credentials. It must be done the "right way" to count and receive the right praise and approval. Circumcision that brings God's praise and approval is simply indicated by a changed heart, that is, one that is joyfully obedient and loving toward God. It may or may not have the right credentials or behaviors with it.
This circumcised life which brings each person into the community of Christ is not done by the person themselves, but is accepted by the person. The old way of life must be cut off and the new life in Christ must be accepted and lived. Otherwise, it will be as with the Jews that Paul spoke of: "You have become as though you had not been circumcised." This new life must be met with a trust that matches it. It must be embraced and lived from the heart, by the Spirit, and to the praise of God.