Schism

Is defined as, "The refusal to submit to the authority of the Pope or to hold communion with members of the Church subject to him. It differs from apostasy and heresy, but often leads to them. Anyone guilty of an external act of schism is ipso facto excommunicated." (Definition from A Catholic Dictionary, 1951)
 

References to Schism in Scripture:

• And other sheep I have, that are not of this fold: them also I must bring, and they shall hear my voice, and there shall be one fold and one shepherd. John 10:16
• And if he will not hear them: tell the church. And if he will not hear the church, let him be to thee as the heathen and publican. Matthew 18:17 (comment: it is through the head bishop that we hear the Church).
• Now I beseech you, brethren, by the name of our Lord Jesus Christ, that you all speak the same thing, and that there be no schisms among you; but that you be perfect in the same mind, and in the same judgment. 1 Corinthians 1:10
• But our comely parts have no need: but God hath tempered the body together, giving to that which wanted the more abundant honor, That there might be no schism in the body; but the members might be mutually careful one for another. And if one member suffer any thing, all the members suffer with it; or if one member glory, all the members rejoice with it. Now you are the body of Christ, and members of member. 1 Corinthians 12:24-27
   

Catholic Church Teaching on Schism in the Church:

• "Wherefore as no heresy can ever be justifiable, so in like manner there can be no justification for schism. "There is nothing more grievous than the sacrilege of schism....there can be no just necessity for destroying the unity of the Church" (S. Augustinus, Contra Epistolam Parmeniani, lib. ii., cap. ii., n. 25). From the encyclical, "ON THE UNITY OF THE CHURCH" by Pope Leo XIII, 1896
• "Heresies and schisms have no other origin than that obedience is refused to the priest of God, and that men lose sight of the fact that there is one judge in the place of Christ in this world" (Epist. xii. ad Cornelium, n. 5). From the encyclical, "ON THE UNITY OF THE CHURCH" by Pope Leo XIII, 1896
• "Between heresy and schism there is this difference, that heresy perverts dogma, while schism, by rebellion against the bishop, separates from the Church. Nevertheless there is no schism which does not trump up a heresy to justify its departure from the Church." (St. Jerome, In Ep. ad Tit., iii, 10).
• "By false doctrines concerning God heretics wound faith, by iniquitous dissensions schismatics deviate from fraternal charity, although they believe what we believe" (St. Augustine, De fide et symbolo, ix)
• "He who abandons the See of Peter on which the Church was founded, falsely believes himself to be a part of the Church." Originally by St. Jerome, and referenced in the Encyclical on Liberalism and Religious Indifferentism by Pope Gregory XVI, 1832.

Catholic Church Teaching on Schism and the Pope:

• “Finally, one cannot consider as schismatics those who refuse to obey the Roman Pontiff because they would hold his person suspect or, because of widespread rumors, doubtfully elected (as happened after the election of Urban VI), or who would resist him as a civil authority and not as pastor of the Church.” (Wernz-Vidal, Ius Canonicum [Rome: Gregorian 1937], 7:398, my emphasis.)
• "Further, if ever at any time it becomes clear that any Bishop, even one conducting himself as an Archbishop, Patriarch, or primate; or any Cardinal of the aforesaid Roman Church, even as mentioned, a Legate; or likewise any Roman Pontiff before his promotion or elevation as a Cardinal or Roman Pontiff, has strayed from the Catholic Faith or fallen into some heresy, [or has incurred, encouraged or incited schism], then his promotion or elevation shall be null, invalid and void." CUM EX APOSTOLATUS OFFICIO, Pope Paul IV, February 15, 1559
• "It shall be lawful for all and sundry who would have been subject to persons so promoted and elevated, had these not first strayed from the Faith or been heretics, or incurred or incited or committed schism; for clerics, secular or regular, and for laymen; likewise for Cardinals, even for those who participated in the election of one straying from the Faith, or of a heretic or schismatic to the Papacy, or who otherwise presented and pledged him obedience and paid him homage". CUM EX APOSTOLATUS OFFICIO, Pope Paul IV, February 15, 1559

Summary

It is clear from Scripture and Church teaching that schism is considered similar to heresy, and neither have ever been acceptable in the Catholic Church. One cannot believe otherwise and remain Catholic!