I should ask in the paedo only forum but I will ask here - if the faith of the parents in paedo churches is found to be false (i.e. they apostatisize), does it nullify the baptism of the child? (Honest question, never come across the answer so I am curious).
I will forego the prior Q (as rhetorical), and set forth a doctrinal response to this latter.
For the Presbyterian, priority falls on the
speech that belongs to God; or put differently, on the testament of the church acting/speaking in Christ's stead. What is being said in baptism? God promises to save all who put their trust in him alone, are cleansed of their sins, and united to Christ the Mediator; which gospel-declaration is symbolized by the sacrament of baptism. God's speech is not nullified if the professors involved in a baptism turn away from faith in Christ. That God made that promise
by name through his church to a particular baptized individual in the context of his kingdom administration, in no wise makes him a captive to the baptized one irrespective of the outcome of his (said) faith.
As 1Pet.3:21 says, baptism is an "answer," a reply/response when considered from the standpoint of the recipient, a secondary speech coming from man (following the dialogical principle). That answer comes both at the hour of personal baptism, and repeatedly as baptism is improved by the recipient. Hence, though an infant does not personally respond (that we can tell) at the hour of his baptism, he must in due time confess Christ and take up the duties of a mature Christian, and partake in the privilege of the Table sacrament. He should make use of his baptism, particularly as he comes to the Table and when he participates (by observation or otherwise) in the baptisms of all others he witnesses.
When a baptized person apostatizes, in the Presbyterian reckoning he is still baptized. Our theology does not reconsider
whether he was, properly, a candidate for baptism; and then conclude (as he persists in unbelief) that being an improper candidate
he was not in fact baptized. Rather, though he was an improper candidate, he was at that time still, in fact baptized. In the same way, and for the same basic reason, the infant who was baptized by professing believers who later abandoned the faith still possesses the record of God's witness, his public claim to "ownership" and the imposition of his Name on that property.
Regardless of who one is, or the status of his personal faith, or when he was baptized--the act of despising a gospel declaration, not the words only but also the demonstration and exhibition of the mercy of God in tangible, sensible form by baptism--this is an atrocity. It is a public execration of God's stamp of ownership. Yes, every created thing has an indelible mark from the Creator; but a baptism is a step further. It has the character of God's open declaration to all that he is the Redeemer, that he would redeem everyone who belongs to his company, everyone who publicly takes his sign-and-seal and bears his Name. Some people hate their country in their hearts; others burn their country's flag on camera.
A child who was baptized on account of the supposed faith of one-time professors, now bears that claim. He should not repudiate it, but affirm it all his life, just as he should if he for the first time and on his own account presented himself for baptism as a mature person. How sweet to know, if later in life, that one taken from the church by parents who turned back, should he return on his own he will say that God had not only known him from before the creation of the world: he also marked him as his property long prior to this late return, only now acknowledged after such a space.