[update]Nathaniel Cooley pointed me to Mark A. Herzer’s article, The Church: A Covenant Community. The thrust of the article centers on the importance of the local church and membership therein. The latter part of the lengthy (33 pages) article addressed the Presbyterian notion of membership.
Herzer writes that the Presbyterian has always understood the visible/local church to be a mixed body. This was true of the Old Testament people of God and it is true of the New Testament people of God. Unlike the Baptist’s, the Presbyterian does not seek to remove the proverbial “wheat from the tares.” On page 27 he claims that the membership of the local body/church is made up of believers and their progeny. On page 25 he writes that the requirement for membership is a credible confession, not regeneration.
This does not mean that anyone and everyone can be a member. The operative phrase on page 25 was credible confession. I would assume that there would come a time in the life of a believer’s child when he would have to confess Christ. It would also be my assumption that a non-credible confession would bar membership in the local church and that out-right rejection of Christ is the OT equivalent of “being cut-off” from the covenant community.