What many may know but forget, is that the English Baptists came out of a period they called "The Great Tribulation from 1660 to 1688. That Period was when the Catholics were in control of the throne of England and both Baptists and Presbyterians were equally persecuted and had to hide and often were found hiding together.
In 1688 the throne of England fell into the hands of the Presbyterians and the Baptists intentionally designed their 1689 confession of Faith after the pattern of the Westminister Confession for one particular reason - to show that they were orthodox in their beliefs with the hope that the Presbyterians would not persecute then as did the Catholics. In 1688 the new powere granted a religous toleration act which gave further hope to the Baptists.
Now, if you really want to understand what the 1689 Baptists meant by their article on the church, then just carefully compare the contrasting features with the Westminister Confession article on the church.
Language must be defined in its historical context and that is only way you will properly understand what these Baptists believed and did not believe in contrast to the Presbyterians. When it is carefully examined, you will see they had not changed their belief on the church at all from their early London Confession of faith, but very tactfully agreed with all the langauge of the Westminister they could but redefined the terms to fit their own beliefs.
Notice the contrast between Article 1 in the Westminister compared to article 1 in the 1689 London confession.
First the Westminister:
"I. The catholic or universal Church, which is invisible, consists of the whole number of the elect, that haven been, are, or shall be gathered into one, under Christ the head thereof: and is the spouse, the body, the fullness of Him that fills all in all.
Now the 1689 Baptist:
I. The catholic or universal church, which (with respect to the internal work of the Spirit and truth of grace) may be called invisible, consists of the whole number of the elect......
The parenthetical explanation is important when you read the contrasts between the Baptist and Westminister in sections 2-5.
However, the contrast between the two confessions is really highlighted by the Baptists in Article 2.
First the Westminister:
2. The visible Church, which is also catholic or universal under the Gospel (not confined to one nation, as before under the law), consists of all those throughout the whole world that profess the true religion; tion.[and of their children; and is the kingdom of the Lord Jesus Christ, the house and family of God, out of which there is no ordinary possibility of salva/I]
Now, the Baptist:
2. All Persons throughout the world professing the faith of the gospel, and obedience unto God by Christ according unto it, not destroying their own profession by any errors everting the foundation, or unholiness of conversation, are and may be called visible saints, and fo scuh ought all partcular congregations to be constituted.
First notice how the Presbyterians define "catholic" = "not confined to one nation, as before under the Law".
Notice also, that the Westminister defines "church" to consist "of all those throughout the world that profess the true religion."
I would say you probably interpreted article one in both confessions to agree with this Westminister definition of Catholic. However, the Baptists did not agree with that definition of the "church".
The Baptist Confession takes issue with both of these points. (1) Baptist refused to call all beleivers in the world "the church," instead, they said "all persons throughout the world professing the faith....may be called visible saints." (2)Baptist refused to define the church as being constituted of such saints, who did not embrace essential errors contrary to the faith, or were ungodly.
In sections three and four the Baptists condemned all churches that contained such error as "no churches of Christ" but "synogogues of Satan" and called the Pope "the antichrist."
In other words these Baptist (consisting over 100 churches) in section 2 rejected the Protestant Reformed concept of a universal invisible church made up of all saints, in all denomination worldwide.
Positively, they did believe in the future glory church made up of all true believers as section one states. Section one does not assert any PRESENT existence of this church but rather speaks of its as the "whole body" that "shall be gathered" consisting of all that have been and are true Christians.
However, this future glory church is then defined by section 2 as including all that are in true churches now. They denied that pedobaptist churches consisted of born again members. and that is why they carefully defined members of this glory church as excluding those within what they called Babylon the Great Whore.
When their minutes of their associations are studied it will be seen that this singular church was believed to contain only those truly saved within what they regarded as saved members of their own kind of churches. I can substantiate this by the associational records of Early English Baptists.