Audio commentary on this verse

Note 4 at Rom. 4:11: The rite of circumcision was a confirmation (see ref. h and ref. i at this verse) of the righteousness that Abraham already had attained by faith. It was meant to be a constant reminder to him of the covenant between God and himself. It was never intended to be something that Abraham would boast about or use to show others his holiness. This was private!

No doubt one of the reasons the Lord chose this act as a sign of the covenant instead of some other act was to prevent the very thing that the Jews were doing. How were you to tell if someone else was circumcised? That's not the kind of thing that is public knowledge. It's between God and that individual. God gave the sign of circumcision because it is a very private act, therefore, He never intended us to use circumcision to judge the righteousness of anyone.