Schism is a very serious word. Being called a schismatic is a very serious charge. It means to break away from a group and form a new group. There is a need for unity but only that which is based in sanctity and truth (see Jesus’ High Priestly Prayer in John 17).
Sometimes groups start very well. But they often become man-centered rather than God honoring. So once in a great while schism is justified.
Once such situation is the Protestant Reformation where people like Martin Luther and John Calvin spoke the truth from the Bible. Luther did not want to leave the Roman Catholic Church, but it happened.
In the case of John Calvin, he had left Geneva (he was later invited back) and was happily pastoring French Protestants in the northern city of Strasbourg when a Catholic leader named Sadolet wrote a letter to the Genevan Council trying to get that city to return to Catholicism. The council sent the missive to Calvin who replied.
In his “Reply to Sadolet” Calvin is very persuasive in many ways. He responds to Sadolets charge of being a schismatic.
“As to the charge of forsaking the Church, which they were wont to bring against me, there is nothing of which my conscience accuses me, unless, indeed, he is to he considered a deserter, who, seeing the soldiers routed and scattered, and abandoning the ranks, raises the leader’s standard, and recalls them to their posts. For thus, O Lord, were all thy servants dispersed, so that they could not, by any possibility, hear the command, but had almost forgotten their leader, and their service, and their military oath. In order to bring them together, when thus scattered, I raised not a foreign standard, but that noble banner of thine whom we must follow, if we would be classed among thy people.”
Since the days of the Reformation and especially since Vatican 2 in the 1960s, Catholics and Protestants who choose to do so have grown closer together without giving up their distinctives. We agree on the confession that “Jesus is Lord.” Much follows from that, including one’s view of the Bible.