That the Church is a visible society, consisting of the professors of the true religion, as distinguished from the body of true believers, known only to God, is plain, they say, because under the old dispensation it was such a society, embracing all the descendants of Abraham who professed the true religion, and received the sign of circumcision… The Church exists as an external society now as it did then; what once belonged to the commonwealth of Israel, now belongs to the visible Church...
It is to be remembered that
there were two covenants made with Abraham. By the one, his natural descendants through Isaac were constituted a commonwealth, an external, visible community. By the other, his spiritual descendants were constituted a Church. The parties to the former covenant were God and the nation; to the other, God and his true people.
The promises of the national covenant were national blessings; the promises of the spiritual covenant, (i.e. of the covenant of grace) were spiritual blessings, reconciliation, holiness, and eternal life.
The conditions of the one covenant were circumcision and obedience to the law; the condition of the latter was, is, and ever has been, faith in the Messiah as the seed of the woman, the Son of God, and the Savior of the world.
There cannot be a greater mistake than to confound the national covenant with the covenant of grace, and the commonwealth founded on the one with the Church founded on the other.
When Christ came “the commonwealth” was abolished, and there was nothing put in its place. The Church
remained. There was no external covenant, nor promises of external blessings, on condition of external rites and subjection. There was a spiritual society with spiritual promises, on the condition of faith in Christ. In no part of the New Testament is any other condition of membership in the Church prescribed than that contained in the answer of Philip to the eunuch who desired baptism: “If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God.” (Acts viii. 37)
https://contrast2.wordpress.com/2010/01/26/hodge-on-the-visibility-of-the-church/