FIRST: Here are the teachings of the Catechism Of the Catholic Church:
846 How are we to understand this affirmation, often repeated by the Church Fathers?335 Re-formulated positively, it means that all salvation comes from Christ the Head through the Church which is his Body:
Basing itself on Scripture and Tradition, the Council teaches that the Church, a pilgrim now on earth, is necessary for salvation: the one Christ is the mediator and the way of salvation; he is present to us in his body which is the Church. He himself explicitly asserted the necessity of faith and Baptism, and thereby affirmed at the same time the necessity of the Church which men enter through Baptism as through a door. Hence they could not be saved who, knowing that the Catholic Church was founded as necessary by God through Christ, would refuse either to enter it or to remain in it.336
847 This affirmation is not aimed at those who, through no fault of their own, do not know Christ and his Church:
Those who, through no fault of their own, do not know the Gospel of Christ or his Church, but who nevertheless seek God with a sincere heart, and, moved by grace, try in their actions to do his will as they know it through the dictates of their conscience – those too may achieve eternal salvation.337
848 “Although in ways known to himself God can lead those who, through no fault of their own, are ignorant of the Gospel, to that faith without which it is impossible to please him, the Church still has the obligation and also the sacred right to evangelize all men.”338
EARLY CHURCH FATHERS
Ignatius of Antioch
“Be not deceived, my brethren: If anyone follows a maker of schism [i.e., is a schismatic], he does no inherit the kingdom of God; if anyone walks in strange doctrine [i.e., is a heretic], he has no part in the passion [of Christ]. Take care, then, to use one Eucharist, so that whatever you do, you do according to God: For there is one flesh of our Lord Jesus Christ, and one cup in the union of his blood; one altar, as there is one bishop, with the presbytery and my fellow servants, the deacons” (Letter to the Philadelphians 3:3–4:1 [A.D. 110]).
“In the Church God has placed apostles, prophets, teachers, and every other working of the Spirit, of whom none of those are sharers who do not conform to the Church, but who defraud themselves of life by an evil mind and even worse way of acting. Where the Church is, there is the Spirit of God; where the Spirit of God is, there is the Church and all grace” (Against Heresies 3:24:1 [A.D. 189]).
“[The spiritual man] shall also judge those who give rise to schisms, who are destitute of the love of God, and who look to their own special advantage rather than to the unity of the Church; and who for trifling reasons, or any kind of reason which occurs to them, cut in pieces and divide the great and glorious body of Christ, and so far as in them lies, destroy it—men who prate of peace while they give rise to war, and do in truth strain out a gnat, but swallow a camel. For they can bring about no ‘reformation’ of enough importance to compensate for the evil arising from their schism. . . . True knowledge is that which consists in the doctrine of the apostles, and the ancient constitution of the Church throughout all the world, and the distinctive manifestation of the body of Christ according to the successions of the bishops, by which they have handed down that Church which exists in every place [i.e., the Catholic Church]” (ibid., 4:33:7–8).
“If someone from this people wants to be saved, let him come into this house so that he may be able to attain his salvation. . . . Let no one, then, be persuaded otherwise, nor let anyone deceive himself: Outside of this house, that is, outside of the Church, no one is saved; for, if anyone should go out of it, he is guilty of his own death” (Homilies on Joshua 3:5 [A.D. 250]).
Cyprian of Carthage
“Whoever is separated from the Church and is joined to an adulteress [a schismatic church] is separated from the promises of the Church, nor will he that forsakes the Church of Christ attain to the rewards of Christ. He is an alien, a worldling, and an enemy. He cannot have God for his Father who has not the Church for his mother” (The Unity of the Catholic Church 6, 1st ed. [A.D. 251]).
“Let them not think that the way of life or salvation exists for them, if they have refused to obey the bishops and priests, since the Lord says in the book of Deuteronomy: ‘And any man who has the insolence to refuse to listen to the priest or judge, whoever he may be in those days, that man shall die’ [Deut. 17:12]. And then, indeed, they were killed with the sword . . . but now the proud and insolent are killed with the sword of the Spirit, when they are cast out from the Church. For they cannot live outside, since there is only one house of God, and there can be no salvation for anyone except in the Church” (Letters 61:4 [A.D. 253]).
“When we say, ‘Do you believe in eternal life and the remission of sins through the holy Church?’ we mean that remission of sins is not granted except in the Church” (ibid., 69:2 [A.D. 253]).
“Peter himself, showing and vindicating the unity, has commanded and warned us that we cannot be saved except by the one only baptism of the one Church. He says, ‘In the ark of Noah a few, that is, eight souls, were saved by water. Similarly, baptism will in like manner save you” [1 Peter 3:20-21]. In how short and spiritual a summary has he set forth the sacrament of unity! In that baptism of the world in which its ancient wickedness was washed away, he who was not in the ark of Noah could not be saved by water. Likewise, neither can he be saved by baptism who has not been baptized in the Church which is established in the unity of the Lord according to the sacrament of the one ark” (ibid., 73:11).
“[O]utside the Church there is no Holy Spirit, sound faith moreover cannot exist, not alone among heretics, but even among those who are established in schism” (Treatise on Rebaptism 10 [A.D. 256]).
“Heretics bring sentence upon themselves since they by their own choice withdraw from the Church, a withdrawal which, since they are aware of it, constitutes damnation. Between heresy and schism there is this difference: that heresy involves perverse doctrine, while schism separates one from the Church on account of disagreement with the bishop. Nevertheless, there is no schism which does not trump up a heresy to justify its departure from the Church” (Commentary on Titus 3:10–11 [A.D. 386]).
“We believe also in the holy Church, that is, the Catholic Church. For heretics violate the faith itself by a false opinion about God; schismatics, however, withdraw from fraternal love by hostile separations, although they believe the same things we do. Consequently, neither heretics nor schismatics belong to the Catholic Church; not heretics, because the Church loves God; and not schismatics, because the Church loves neighbour” (Faith and the Creed 10:21 [A.D. 393]).
“[J]ust as baptism is of no profit to the man who renounces the world in words and not in deeds, so it is of no profit to him who is baptized in heresy or schism; but each of them, when he amends his ways, begins to receive profit from that which before was not profitable, but was yet already in him” (On Baptism, Against the Donatists 4:4 [A.D. 400]).
“The apostle Paul said, ‘As for a man that is a heretic, after admonishing him once or twice, have nothing more to do with him’ [Titus 3:10]. But those who maintain their own opinion, however false and perverted, without obstinate ill will, especially those who have not originated the error of bold presumption, but have received it from parents who had been led astray and had lapsed . . . those who seek the truth with careful industry and are ready to be corrected when they have found it, are not to be rated among heretics” (Letters 43:1 [A.D. 412]).
“Whoever is separated from this Catholic Church, by this single sin of being separated from the unity of Christ, no matter how estimable a life he may imagine he is living, shall not have life, but the wrath of God rests upon him” (ibid., 141:5).