The following is a quote from Our Baptist Heritage: Issues Facing Reformed Baptists Today (Reformation Today Trust, 1993) on baptism in relation to the nature of the Church:
The basic issue in the subject of baptism is the nature of Church. Zwingli sought to persuade Blaurock of the validity of infant baptism on the basis of the Abrahamic covenant and circumcision. Baptists, while accepting the doctrine of the covenants (see the 1689 Confession, chapter 7), regard circumcision as symbolic of the need of regeneration. They hold that only those who have a credible profession of faith fulfil the terms of the new covenant. Only those who have the evidence of a new heart and a new spirit qualify for baptism and church membership. Baptists stress both the unity and discontinuity of the covenant administration. They point out that the Scriptures emphasise that the new covenant is different in that it is not national; all without exception are included [in the national model]. ‘It will not be like the covenant I made with their fore-fathers’ (Heb 8:9). Rather the new covenant includes only those who know the Lord, ‘They will all know me, from the least of them to the greatest. For I will forgive their wickedness and will remember their sins no more’ (Heb 8:12). [p. 17]
This, in a nutshell, is the Reformed Baptist perspective and argument. Perhaps its greatest strength is that it embraces the unity or continuity of the covenants, unlike that of Dispensationalism, while at the same time seeking to understand the New Covenant on its own clearly defined terms (the aspects of discontinuity). For a fuller expression of this argument for believer’s baptism (credo-baptism), please see A Reformed Baptist Manifesto: The New Covenant Constitution of the Church.