Piper: The New Covenant "narrow(s)...the covenant people to those who are truly born of God"

"...New Covenant members are not defined by physical descent, as the old covenant members were, but by God's writing his law on their heart and calling them to himself and bringing them to repentance and faith.

"In accord with this narrowing of the covenant people to those who are truly born of God, the new sign of the covenant is meant to signify that a person is indeed part of that new born covenant community, which is evident by faith.
In the same way that a change in the sign came in to allow both men and women to participate in the sign (baptism instead of circumcision), thus making it clearer than before that women and men are equal heirs of salvation (1 Peter 3:7), so also a change in the recipients of the sign came in to make it clearer that under the New Covenant the people of God are not determined at all by physical descent, but by spiritual transformation, evidenced in faith." -- John Piper, "Infant Baptism and the New Covenant Community"