The differences between the Paedobaptists & Credobaptists in regards to the new covenant really boils down to the question of whether there is a mixed people (believers & unbelievers or a covenant community & the remnant) or if the new covenant community is a redeemed people only. The New Covenant community does have unbelievers in it but this should not be something done purposefully. The recipients of the New Covenant privileges and blessings however should only be attributed to a company of regenerate people. The continuity that we see from the Old Covenant to the New Covenant people is not nationalistic but it is a continuation of the remnant. There are no covenant breakers in the New covenant precisely because of the nature of it. In other words it is God who assures the New Covenant blessings upon the people (Jeremiah 31:31-34-Notice the expression “I will).
There are those from the paedobaptist camp who see that Jeremiah 31 cannot allow unregenerate people as members. They agree, in essence, with Credo Baptists yet they appeal to the “already/not yet” formula to get around it. It is argued that the “already” has a mixed group within it while, at the consummation of all things, the “not yet” will have the entire community of the New Covenant “knowing the Lord”.
The Old Testament community was far different than the New Covenant community is many respects. The Old Covenant community had physical “priests” with whom the people of God had to do as their representatives before God while under the New Covenant we are all “priests”. The leaders have no more bearing upon the suffering of the people due to their sins.
Another very important difference is in regards to the Holy Spirit. Under the Old Covenant, the Spirit of God was poured out but only upon those in leadership (priests, prophets) while under the New Covenant, the Spirit is poured out on all those within the covenant community (Joel 2:28-32; Acts 2). The seal of the covenant is now the Holy Spirit (Ephesians 1:13-14) who works to keep the covenant people as covenant keepers! The New Covenant is not a renewed covenant from the Abrahamic covenant but it is a new and improved covenant precisely due to the promise of the Spirit.