The editors of the confession intentionally avoided addressing open and closed communion in order to allow more churches to be able to subscribe to the confession. The majority of its subscribers were advocates of closed communion, but there had been a strand of open-communion going as far back as Henry Jessey and others among the original Particular Baptists of the 1640’s. To accommodate those, and especially Bunyan, the confession is silent here.
By church-communion is meant “official church membership.”
They explain their rationale below.
Confessions do not exhaustively represent everything that a given church or association holds to be true. For that reason, a line has to be drawn somewhere by which some things are confessed and others not. Unity should be striven for, but never at the cost of truth. In this case the editors extended an olive branch to their open-communion brothers, and exhorted paedobaptists to do the same to them. Remember that through government power (whether controlled by Presbyterians, Independents, or Charles II), the Baptists were persecuted for their view on baptism. Because infant baptism, or christening, was a means of social and political enrollment and enforcement, failure to participate in this process was viewed as a breach of loyalty to the country. You were supposed to be registered in a given parish and required to attend the church of England within that parish. The Baptists did not submit to infant baptism, and they excommunicated their members who left for the church of England. This adds a certain character to their plea for tolerance beyond that of “let’s all get along.”
This is found at the end of the Appendix on baptism.
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