I want to be very clear here: they were not being inconsistent nor were they being "nice".
What I am about to say applies not to all 1689 adherents but enough of us to be a significant number:
We believe there is is only one true baptism and any true church - by necessity - performs true baptisms.
We would see your infant baptism as an invalid mode but still legal, since we would not see
you as an invalid subject based on your subsequent public profession of faith and evidence of fruit of the Spirit to become a communicant member of the PCA, OPC, ARC, RPCNA et al (all true churches in our view).
Another way of saying it is that a true church confirms you qualify as a member of the invisible church with any and all charity as anyone out there can have.
Now if you had been infant baptized into Roman Catholic (which we deny is a true church per Turretin et al), it would depend: did the PCA or whomever accept your Roman infant baptism as legal and then you subsequently publicly professed faith becoming a legal - and valid - communicant member of the PCA or any other true church? Then I would be ok with no re-baptism (honestly not sure about all elders).
But if there comes one who was baptized as an infant in a true Presbyterian church, but by the age of 2, their parents left church altogether and that person never went back - stunted in their walk - but now after that time long ago, came to us energetically asking to be a member, then we would probably ask for re-baptism - not necessarily because his first baptism was an infant baptism in and of itself - but as there is no real verification from a true church about what happened over time.
ie invalid mode, invalid subject and no validation over time by a true church = illegal.
(I suppose even the paedobaptists would halt his enthusiasm and look hard and then assess whatever means you have for assessing the profession of saving faith as well before letting him to the Table.)
Do we deny the Lord's Table is truly the Lord's Table in the PCA or OPC etc? Simply because no one (or very few) were baptized as self-aware professors of Christ? We do not.
That seems to put too much weight on the distinctives and not enough charity for the obvious fact that our Lord's love covers a multitude of sins of errors - and that is evidently true in all of us - and that is no matter which one of us turns out to be right when we worship around his throne!
I mean, a "re-baptism" per se is
never necessary for it is only recommended in cases where we are truly convicted
no real baptism ever took place (Rome/ EO / infant Presbyterian who cut themselves short of public profession with evidence of saving grace / "Oneness" Pentecostals who only baptize in the name of Jesus as they deny the Trinity / etc etc etc)
This is not novel either. Nor unique to me. It is rather historical.
Beyond Bunyan receiving infant baptized as members (and he was never confessional anyway), the Particular Baptists wrote 29.4 as "Immersion, or dipping of the person in water, is necessary to the due administration of this ordinance."
Why allow for the other mode?
"Other modes of baptism are undue actions. ... 'Due' [as used in the 2LBCF] ... has the same sense [in previous uses] indicating that there is a proper, and also an improper way to baptize. Immersion is the
proper form; by implication, other methods are improper. This may reflect the post-Reformation concept between
valid and
lawful baptisms: an action may be improper but still legal." - Jim Renihan (pp. 549, 550)
He then quotes a Scottish theologian named James MacPherson:
"so little disposed were the divines of Scotland (and other Reformed churches) to question the validity of baptism administered within any Christian church that they even declined to pronounce baptism administered by a deposed minister as invalid, and rather introduced a distinction, useful though somewhat fine, between a valid and a lawful baptism. The action of the deposed minister and the conduct of those receiving baptism at his hands was distinctly unlawful, but the baptism itself was valid, and as such could not be ignored ..."
Renihan continues from p. 550 - 551:
"The appendix to the [1689] Confession recognizes that paedobaptist churches are true congregations of Christ. After expressing their doctrinal agreement with paedobaptist churches, they say:
'And although we differ from our brethren who are Paedobaptists, in the subject and administration of Baptisme, and such other circumstances as have a necessary dependence on our observance of that Ordinance, and do frequent our own assemblies for our mutual edification and discharge of those duties and services we owe unto God, and in his fear to each other: yet we would not be from hence misconstrued, as if the discharge of our own consciences herein did any wayes disoblige or alienate our affections, or conversation from any others that fear the Lord; but that we may and do as we have opportunity participate of the labors of those, whom God hath indued with abilities above ourselves and qualified and called to the Ministry of the Word, earnestly desiring to approve ourselves to be such as follow after peace with holiness, and therefore we always keep that blessed Irenicum or healing Word of the Apostle before our eyes; if in anything ye be otherwise minded, God shall reveal this unto you; nevertheless whereto we have already attained; let us walk by the same rule, let us mind the same thing. [
Phil. 3:15,
16]' ... They clearly regarded paedobaptist churches as true churches and were well aware of the issues surrounding baptism ... It seems .. that while they themselves would only practice immersion as the due method of administration, at least some of the churches could receive members who may not have been baptized by
due means." (italics original to Renihan, not me)
Renihan then goes to relate Nehemiah Coxe's Petty France church receiving a woman from a Pinners' Hall Independent church.
Also, he writes of:
"Broadmead, Bristol accepted a letter of membership transfer for their new pastor's wife from a Presbyterian congregation in London. And the Stevington, Bedfordshire Particular Baptist assembly received a woman from an Independent church in Newport Pagnell, Buckinghamshire. There is no indication that baptism was required of these people when they joined these assemblies." (Renihan 551)
He cites their records:
"Petty France, CMB. Hayden,
The Records of a Church of Christ, 186. The London Presbyterian church's pastor was Thomas Vincent. The letter indicated that the Presbyterian church admitted members: 1 Upon Enquiry of ye parties' knowledge of God and ye Doctrine of Salvation. 2. Upon Enquiry of ye Work of Grace upon their Hearts. 3. Upon Enquiry of a Good and Blameless Conversation. The Broadmeade scribe says that this was 'as wee doe'
(He isn't specific but Renihan seems to be suggesting that the Pastor Thomas Vincent downplays the infant baptism and kind of rolls into number 2 allowing Broadmead to reply that they do likewise (number 2) while the issue of her (the wife coming over) baptism is kind of waved away)