Lucius of Castra Galbae said: Since the Lord in His Gospel said, “You are the salt of the earth: but if the salt should have lost its savour, wherewith shall it be salted? It is thenceforth good for nothing, but to be cast out of doors, and to be trodden under foot of men.” And again, after His resurrection, sending His apostles, He gave them charge, saying, “All power is given unto me, in heaven and in earth. Go and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost.” Since, therefore, it is manifest that heretics— that is, the enemies of Christ— have not the sound confession of the sacrament; moreover, that schismatics cannot season others with spiritual wisdom, since they themselves, by departing from the Church, which is one, having lost the savour, have become contrary to it—let it be done as it is written, “The house of those that are contrary to the law owes a cleansing.” And it is a consequence that those who, having been baptized by people who are contrary to the Church, are polluted, must first be cleansed, and then at length be baptized.
Crescens of Cirta said: In such an assembly of most holy fellow priests, as the letters of our most beloved Cyprian to Jubaianus and also to Stephen have been read, containing in them so much of the holy testimonies which descend from the divinely made Scriptures, that with reason we ought, all being made one by the grace of God, to consent to them; I judge that all heretics and schismatics who wish to come to the Catholic Church, shall not be allowed to enter without they have first been exorcised and baptized; with the exception of those indeed who may previously have been baptized in the Catholic Church, and these in such a way that they may be reconciled to the penitence of the Church by the imposition of hands.
Nicomedes of Segermae said: My opinion is this, that heretics coming to the Church should be baptized, for the reason that among sinners without they can obtain no remission of sins.
Munnulus of Girba said: The truth of our Mother the Catholic Church, brethren, has always remained and still remains with us, and even especially in the Trinity of baptism, as our Lord says, “Go and baptize the nations, in the name of the Father, of the Son, and of the Holy Spirit.” Since, then, we manifestly know that heretics have not either Father, or Son, or Holy Spirit, they ought, when they come to the Church our Mother, truly to be born again and to be baptized; that the cancer which they had, and the anger of damnation, and the witchery of error, may be sanctified by the holy and heavenly layer.
Secundinus of Cedias said: Since our Lord Christ says, “He who is not with me is against me;” and John the apostle calls those who depart from the Church Antichrists— undoubtedly enemies of Christ— any such as are called Antichrists cannot minister the grace of saving baptism. And therefore I think that those who flee from the snares of the heretics to the Church must be baptized by us, who are called friends of God, of His condescension.
Felix of Bagai said: As, when the blind leads the blind, they fall together into the ditch; so, when the heretic baptizes a heretic, they fall together into death. And therefore a heretic must be baptized and made alive, lest we who are alive should hold communion with the dead.
Polianus of Mileum said: It is right that a heretic be baptized in the holy Church.
Theogenes of Hippo Regius said: According to the sacrament of God's heavenly grace which we have received, we believe one baptism which is in the holy Church.
Dativus of Badis said: We, as far as in us lies, do not hold communion with heretics, unless they have been baptized in the Church, and have received remission of their sins.
Successus of Abbir Germaniciana said: Heretics can either do nothing, or they can do all. If they can baptize, they can also bestow the Holy Spirit. But if they cannot give the Holy Spirit, because they have not the Holy Spirit, neither can they spiritually baptize. Therefore we judge that heretics must be baptized.
Fortunatus of Tuccaboris said: Jesus Christ our Lord and God, Son of God the Father and Creator, built His Church upon a rock, not upon heresy; and gave the power of baptizing to bishops, not to heretics. Wherefore they who are without the Church, and, standing in opposition to Christ, disperse His sheep and flock, cannot baptize, being without.
Sedatus of Tuburbo said: In the degree in which water sanctified in the Church by the prayer of the priest, washes away sins; in that degree, if infected with heretical discourse as with a cancer, it heaps up sins. Wherefore we must endeavour with all peaceful powers, that no one infected and stained with heretical error refuse to receive the single and true baptism of the Church, by which whosoever is not baptized, shall become an alien from the kingdom of heaven. Privatianus of Sufetula said: Let him who says that heretics have the power of baptizing, say first who rounded heresy. For if heresy is of God, it also may have the divine indulgence. But if it is not from God, how can it either have the grace of God, or confer it upon any one?
Privatus of Sufes said: He who approves the baptism of heretics, what else does he do than communicate with heretics?
Hortensianus of Lares said: Let either these presumptuous ones, or those who favour heretics, consider how many baptisms there are. We claim for the Church one baptism, which we know not except in the Church. Or how can they baptize any one in the name of Christ, whom Christ Himself declares to be His adversaries?
Cassius of Macomadae said: Since there cannot be two baptisms, he who yields baptism to the heretics takes it away from himself. I judge therefore that heretics, lamentable and corrupt, must be baptized when they begin to come to the Church; and that when washed by the sacred and divine washing, and illuminated by the light of life, they may be received into the Church, not as enemies, but as made peaceful; not as foreigners, but as of the household of the faith of the Lord; not as children of adultery, but as sons of God; not of error, but of salvation; except those who once faithful have been supplanted, and have passed over from the Church to the darkness of heresy, but that these must be restored by the imposition of hands.
Another Januarius of Vicus Caesaris said: If error does not obey truth, much more truth does not consent to error; and therefore we stand by the Church in which we preside, that, claiming her baptism for herself alone, we should baptize those whom the Church has not baptized.
Another Secundinus of Carpi said: Are heretics Christians or not? If they are Christians, why are they not in the Church of God? If they are not Christians, how come they to make Christians? Or whither will tend the Lord's discourse, when He says, “He that is not with me is against me, and he who gathers not with me scatters?” Whence it appears plain that upon strange children, and on the offspring of Antichrist, the Holy Ghost cannot descend only by imposition of hands, since it is manifest that heretics have not baptism.
Victoricus of Thabraca said: If heretics are allowed to baptize and to give remission of sins, wherefore do we brand them with infamy and call them heretics?
Another Felix of Uthina said: Nobody doubts, most holy fellow priests, that human presumption is not able to do so much as the adorable and venerable majesty of our Lord Jesus Christ. Therefore, remembering the danger, we ought not only to observe this also, but moreover to confirm it by the voice of all of us, that all heretics who come to the bosom of Mother Church should be baptized, that thus the heretical mind that has been polluted by a long decay, purged by the sanctification of the layer, may be reformed for the better.
Source: The Seventh Council of Carthage (New Advent)