Baptism pertains to the Church alone.

Their property held them in chains...chains which shackled their courage and choked their faith and hampered their judgment and throttled their soul...If they stored up their treasure in heaven, they would not now have an enemy and a thief within their own household...They think of themselves as owners, whereas it is they rather who are owned: enslaved as they are to their own property, they are not the masters of their money but its slaves.

Custom is often only the antiquity of error.

As to what pertains to the case of infants: You [Fidus] said that they ought not to be baptized within the second or third day after their birth, that the old law of circumcision must be taken into consideration, and that you did not think that one should be baptized and sanctified within the eighth day after his birth. In our council it seemed to us far otherwise. No one agreed to the course which you thought should be taken. Rather, we all judge that the mercy and grace of God ought to be denied to no man born

"If any man thirst, let him come and drink from the rivers of living water" (cf. John 7:38). Where shall he who thirsts come? To heretics where the fountain and river of water is in no way life-giving? Or to the Church, which is One?

If, in the case of the worst sinners and those who formerly sinned much against God, when afterwards they believe, the remission of their sins is granted and no one is held back from baptism and grace, how much more, then, should an infant not be held back, who, having but recently been born, has done no sin, except that, born of the flesh according to Adam, he has contracted the contagion of that old death from his first being born. For this very reason does he [an infant] approach more easily to receive the remission of sins: because the sins forgiven him are not his own but those of another

Whereas there can be but one Baptism, they think they can Baptize; they have abandoned the fountain of life, yet promise the life and grace of the waters of salvation. It is not cleansing which men find there, but soiling; their sins are not washed away, but only added to. That being "born again" does not bring forth sons to God but to the Devil. Born of a lie, they cannot inherit the things which Truth has promised; begotten by the faithless, they are deprived of the grace of faith.