The schism comes from people who are trying to enforce various traditional doctrines. In the Presbyterian case, which I know the best, there's not just one traditional denomination, but several. Protestantism as a whole shows how narrow doctrinal standards, without a way to coerce the losers, results in fragmentation.
The thing is, of the various Presbyterian denominations in the US, such as the PCA, OPC, the RPCNA, the PCUSA and the newly formed Evangelical Covenant Order, well, only the PCUSA and the ECO have been derived from a recent schism. Likewise, if we look at the Lutheran churches, it is not a case of parishes leaving the Missouri Synod or one of the other traditional Lutheran churches, to join the NALC, but rather people leaving the ELCA. And in the world of Anglicanism, the Reformed Episcopal Church, which dates from a 19th century schism over objections to the at the time increasingly High Church and Anglo-Catholic Protestant Episcopal Church, and which is a conservative denomination, has not recently suffered a schism but has instead reunited with dioceses of its former congregation as a part of ACNA, despite many of those dioceses being very high church. So, recently, the main cause of schism has been the failure of the mainline churches to make a commitment to Biblical morality.
And frankly, I can’t call the departing congregations, classes, presbyteries and dioceses “schismatic” because if a parish or diocese or presbytery is a member of a larger denomination that makes a radical change in its doctrine that takes it outside of the realm of traditional Christian doctrine concerning human sexuality and other issues, including in the ELCA the extreme situation cause by the existence of parishes like Ebenezer Lutheran, which I have brought up before, Galatians 1:8 seems to compel action.
I agree that the Catholic Church often allowed a degree of disagreement, although there were limits that look pretty narrow by my standards. A smarter or less corrupt pope could probably have avoided a split in the 16th Cent without doing violence to the tradition.
The real proximate cause of the schismatic process, I would argue, was not the corruption of Leo X and his failure to deal with Martin Luther, but the precedent set for what Luther attempted by the Moravians, who, in a desire to reclaim that which they had lost when forcibly converted to the Roman Rite following the conquest of the Czech Lands and Slovakia by Austria (something which later became against RC procedure, hence instead the large Ukrainian Greek Catholic Church, etc). The Moravians and the smaller and older and somewhat less orthodox Waldensians suffered terrible persecution, but they survived, and this allowed Luther to act and survive. And he saw himself as returning to a lost tradition.
Also one cannot really say that much divergence of opinion was tolerated in the Roman Catholic Church during the dark years of the Avignon Papacy, the corrupt Borgias, the militancy of Julius II, and the corrupt misrule of Leo X, because this was the era of the Inquisition. Indeed even in our shared Reformed Calvinist heritage I expect you and me both regard John Calvin’s baiting of Servetus to Geneva so that he could be executed for heresy, and the subsequent decision of the City Council, contra Calvin, to burn Servetus at the stake, with a certain horror, but this was learned behavior, from the Inquisition, and can be interpreted as an attempt by the Reformed Church in Geneva and the theocratic civic authorities to prove their doctrinal orthodoxy in the strongest possible way, based on what were, alas, at the time, the established practices of Western Christianity, which did fortunately become disestablished perhaps as a benefit of some aspects of Enlightenment thinking.
The modern Catholic church seems to have learned that lesson. The Catholic Church in the US is in effect a mainline Protestant denomination with a thin veneer of traditional sexual and gender positions.
And in terms of average attendance at individual services as a percentage of the total capacity of the parish, the traditional, diocesan Latin Mass services which have become relatively widespread after Summorum Pontificum outperforms those of Novus Ordo services.
