External appearances are all that we can see.  Religion, wherever it may be found, tends to accumulate external symbols, rites and ceremonies which are considered 'essential' for anyone who wants to be a part of it.  That was the Jewish background too.  When some Jews believed in Jesus as the Messiah, they wrongly thought the signs guaranteed their salvation.

Circumcision was one of those signs.  It represented a person being ‘cut-out’ to be holy to the Lord.  It was a God-given sign of the old covenant of God's love to those who loyally obeyed Him.  But faithful obedience can never be created by cutting flesh.  Deuteronomy 30:6 recognises that; only the Holy Spirit can change our desires so that we forsake all other gods and only serve the Lord only.  

By saying, “ … a person is a Jew who is one inwardly …” Paul reflects on Deuteronomy 30:30 and anticipates Romans 11:17-24 - where he explains that God’s true people are both Jews and Gentiles who have been incorporated into the same family of God.  He illustrates this by a tree stem into which a different variety is grafted.  Both the original and the grafted shoots derive their life from the same source.  Unfruitful original branches are cut away, but fruiting branches are kept, and the new fruiting spurs are grafted in.  All who derive their life from the stem are equal.  Jesus used a similar analogy saying that He is the vine stem and all who trust and obey His words are the fruiting branches.  They will be pruned back to help them grow stronger, but the unfruitful branches will be removed.  Their right to be in God’s family depends only on their relationship with the stem, who is Jesus (John 15:1-8).  

All those who come in repentance to Jesus have already started that sort of 'heart circumcision'.  External signs cannot save us: only faith in Christ (Ephesians 2:8-9).  There is no external way to mark a humble and contrite heart.  But God can see it ... and that is enough!  2 Timothy 2:19 says, "God's solid foundation stands firm, sealed with this inscription: ‘The Lord knows those who are his,’ and, ‘Everyone who confesses the name of the Lord must turn away from wickedness’."