Here the Apostle Paul, a pharisee (high ranking jewish scholar) by training, is saying that the true cicumcision is spiritual and is a matter of the heart and not a physical thing at all. This is nothing new really, and did not start in the New Testament. As far back as we have the recorded word of God was this made evident.
"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." (Deut 30:6)
"Circumcise therefore the foreskin of your heart, and be no more stiffnecked." (Deut 10:16)
"Circumcise yourselves to the LORD, and take away the foreskins of your heart, ye men of Judah" (Jer 4:4)
Like so many things in the Old Testament, circumcision was a symbol to show a spiritual truth and was not that truth. Righteousness is the result of faith as demonstrated by Abraham before there was any such thing as a Jew. They were Hebrews. The act of circumcision was given as a sign, a symbol of what was already supposed to have taken place spiritually.
It is not automatic. There is no such thing as automatic when applied to God's righteousness. God's righteousness is found in the receipt of grace from the ultimate blood sacrifice of Jesus on the cross for the remission of sins, and is an act of faith on the part of the individual.
Ishmael, the father of all Arabs, and the son of Abraham, was also circumcised (Gen 17:26). It was a symbol of faith, not unlike the symbols we see in many denominations today, the most prevalent being that of a fish. The symbol of the fish doesn't make of you a righteous person before God any more than slicing off a piece of your annatomy. It is what goes on in the heart that makes the difference. That is where the true "circumcision" takes place, in the spirit of the individual.
The apostle Paul spent a good deal of time trying to explain all this to the newly formed Christian churches (assemblies) of the New Testament. Himself being a professional of the "law" and knowing it quite intimately, tried to show how that Jesus was the ultimate sacrificial lamb offered for the sins of the world and that righteousness before God could only come through acceptance of His blood sacrifice. This practice of blood sacrifice was also nothing new, as it was laid out as a ceremony performed by the high priest once per year in what was called the "holy of holies", a secondary chamber reserved for this purpose, and was again a symbol of purification from sin.
This is why when Jesus died on the cross the Bible says that, "And the veil of the temple was rent in twain from the top to the bottom."(Mk 15:38) This "veil" was the one leading to this "holy of holies" and was torn from top to bottom signifying that now Jesus had become this high priest and had performed the ultimate blood sacrifice for the remission of sins for all that will come to Him, ending the need for ceremonialisms and the priesthood, Himself now being the high priest and ordaining whom He will as prophets and teachers and "priest" of the new covenant.
Since the advent of this event there is no such thing as a "chosen people" based on racial, ethnic or geographical location. Jesus said," Ye have not chosen me, but I have chosen you, and ordained you, that ye should go and bring forth fruit, and that your fruit should remain: that whatsoever ye shall ask of the Father in my name, he may give it you."(Jn 15:16)
He it is that is the ultimate high priest that has paid the ultimate price for the ultimate prize, the souls of men ! "But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name." (Jn 1:12). The new covenant that God has made with man for his ultimate Salvation is based in the blood of His Son Jesus Christ, and not in any other ethnic, racial or geohraphical considerations. Salvation is offered to all of mankind regardless of skin colour or lineage (descent in a line from a common progenitor -Webster's) or genetics.
Armed with this information, what will your choice be ? At the moment the choice is still voluntary and offered freely, but the day is coming that it will not be voluntary, only then it may be too late as the Bible says that there will be weeping and gnashing of teeth. "That at the name of Jesus every knee should bow, of things in heaven, and things in earth, and things under the earth; And that every tongue should confess that Jesus Christ is Lord, to the glory of God the Father.." (Phil 2:10-11)