Sometimes, a Christian community is willing to tolerate a variety of beliefs and practices within its borders. But sometimes it is not, and then schisms occur.
Actually, imposed liturgical changes have caused nearly all enduring schisms since the Chalcedon-adjacent schism (which occurred due to a political vendetta against Pope Dioscorus in which the Oriental Orthodox were falsely accused of being the Monophysite followers of Eutyches despite DIoscorus literally having anathematized Dioscorus) have either been related to or derived from imposed changes in worship, which was also a contributing factor in the Nestorian schism (Nestorius devised his warped Christology by borrowing from the some of the more problematic writings of Theodore of Mopsuestia in an attempt to justify having persecuted with violence those who used the phase “Theotokos” to describe the Blessed Virgin Mary, and thus the Council of Ephesus upheld that yes, St. Mary is the Mother of God since there is no way to separate Christ’s humanity from His divinity without rejecting the Incarnation and engaging in crypto-Arianism, with the subsequent Council of Chalcedon needed to clarify that we also cannot conflate, confuse, or declare Christ to be the result of a synthesis of humanity and deity, since that also does violence to the Incarnation - the Oriental Orthodox agree with this premise and while they are using the Miaphysite formulation, this is less different from the Chalcedonian formulation than one might think - specifically it boils down to one word, Chalcedon says Christ is in two natures and the OO say he is fully human and fully divine, from those two natures, while affirming that He is human and divine without change, confusion, separation or division. Indeed the main Christological hymn used to uphold Orthodoxy in the East, Ho Monogenes, was most likely written by St. Severus of Antioch.
Now Lutheranism was not over a liturgical divide primarily although it developed liturgical consequences, but subsequent schisms including the lamentable but largely healed Nikonian schism in the Russian Orthodox Church, and the Old Calendarist schism caused by the imposition of the Revised Julian Calendar on the Eastern Orthodox, and the 1969 Novus Ordo Missae caused a schism with the SSPX which recently became a hot schism again thanks to Leo XIV (there is an eerie correlation with Popes named Leo and schisms - Leo I was at Chalcedon and his Tome contributed to the confusion, Leo IX was the Pope who presided over the beginning of the schism with the Eastern Orthodox, Leo X can be regarded as bearing substantial responsibility for the Lutheran schism because while Pius V had the moral courage to reject the sale of indulgences at the Council of Trent, Leo X decided to just try to stamp out Luther with Exsurge Domine, and Leo XIII was Pope during the declaration of Papal Infallibility) - until the recent excommunication technically the SSPX was not schismatic thanks to the work towards reconciliation by Pope John Paul II and Pope Benedict XVI, which was initially continued by Pope Francis before opposition to him from traditional Catholics over an incident which if I recall was related to the Amazonian synod and which was regarded by traditionalists as idolatry presaged Traditionis Custodes, and then of course we have your own church’s schism in 1979 over the new BCP with the Continuing Anglicans, although that’s been an unusually friendly, very civilized schism, with, for example, the Episcopal Diocese of Las Vegas having very good relations with the local Anglican Province of Christ the King parish, whereas meanwhile I recall reading on the website of the Roman Catholic diocese of that city a warning about schismatic churches back in 2018 which included SSPX chapels despite the fact that at the time they were not excommunicate nor schismatic, officially at least. They are now however.
Relatively few schisms can be attributed to religious persecution by the government of a country - the Old Believer schism being a rare example.
Indeed a lack of an official state religion makes schism much easier, since in the US the First Amendment, which I support, guarantees the right of congregations to separate for any reason no matter how silly although the real estate can become a thorny entanglemenet.