Here are what some of the Church Fathers have to say about this:
Ignatius of Antioch
“Be not deceived, my brethren: If anyone follows a maker of schism *, he does not inherit the kingdom of God; if anyone walks in strange doctrine *, 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]).
“[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 *” (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]).
“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 neighbor” (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]).
“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).***