So, if Paul contends that it is not about possessing the Torah but doing the Torah, who then is the “true Jew”? Paul’s words in Romans 2:25-29, so I think, would have been heard as nothing short of shocking:

Circumcision indeed is of value if you obey the law; but if you break the law, your circumcision has become uncircumcision. So, if those who are uncircumcised keep the requirements of the law, will not their uncircumcision be regarded as circumcision? Then those who are physically uncircumcised but keep the law will condemn you that have the written code and circumcision but break the law. For a person is not a Jew who is one outwardly, nor is true circumcision something external and physical. Rather, a person is a Jew who is one inwardly, and real circumcision is a matter of the heart—it is spiritual and not literal. Such a person receives praise not from others but from God.

Circumcision, the decisive act whereby a male (usually unconsciously as an infant) entered into the covenant community of Israel, is seen by Paul as nothing more than an outward act that is of absolutely no use if the person doesn’t practice the Torah, and it is not needed (does he really say this?) if one does practice the Torah. So, as he says in Galatians 5:6, neither circumcision nor uncircumcision matters; what matters is faith working through love. Now in Romans 2 he puts the same idea in a slightly new form: real circumcision is of the heart. It is about the Spirit of God, not about following Torah.
Tom Wright is right here: Paul is probing forward here with a central concern if his, namely, on what grounds the Gentile enters the family of God. As he will say in Romans 10:5-12, it is about confessing that Jesus is Lord. And it does not matter who it is: Gentile or Jew. All are at level ground now. God’s people are no longer defined by national membership.
The act whereby a Jew divided himself (and his family, including females) from Gentiles, the act of circumcision, is hereby done away with for Paul because it divides physically and does not have the capacity to measure what most matters to Paul: faith in Jesus Christ, the heart, the indwelling of the Spirit.
The background for this doing away with the boundary-marking act of circumcision is very Jewish and very biblical, in fact. You can find it in Deut 30 and Ezekiel 36, not to forget also Jeremiah 31:31-34.