Depends. A schism is a division, but then that particular word is usually used when there is opposition involved, rather than an amiable break.
Lemme think...
Judaism never underwent a single event as a schism, rather had a slow drift resulting in the Orthodox and the Conservative. This drift was largely assisted by the Diaspora, where Jews were spread out and no central authority existed for them.
Verdict: Uncertain
Christianity had a very distinct schism in the 11th century with the development of the Roman Catholic Church and the Eastern Orthodox. Then it could be argued that it happened again come the Reformation, where Western Europe broke into the Roman Catholic Church and Protestant Christians.
Verdict: Schism
Islam had a schism following the death of Muhammad, when his followers argued over whether his children or his closest advisers should inherit the role of leaders of the faith. This was then complicated by the zealous actions of the Turks and the Crusades, which allowed internal and external forces to further subdivide them.
Verdict: Schism
Those of the Baha'i Faith are an interesting predecessor to the idea we would now call Unitarian, although they are certainly not due to their rigid definition of elements they accept from other religions they have contacted and their unwillingness to allow converts. They started as Babs, and a 'rogue' leader gathered up the majority of the followers, giving them a new name and the final definition of what they would become. Although it could be considered a schism that tore them from the Babs, it could also be a new religion, as Islam was considered from Judaism or Christianity.
Verdict: Uncertain
Hmmm... that covers the major Judeo-Christian groups pretty well... I could go into the Eastern, but it's pretty obvious that Hinduism broke into Jainism, Sikhism and Buddhism. And the 'pagan' religions of the West predating Christianity were divided, but their past so lost in a sea of historic illiteracy that it's uncertain whether they suffered from outright disagreements or lack of communication.
The Ancient Egyptian religion (or religions?) would perhaps be the best candidate for a non-schismatic religion. Initially, contact and conquest resulted in the blending of religions, not the destruction or splitting of them. The intermediate periods, times of civil unrest or outside conquest, resulted in social collapses, but the gods and their stories remained intact, only the priests being displaced. Gods preferred by some invaders were not flung aside as a result of disgruntlement, rather given a new place in the pantheon or blended with less desirable gods already in existence. The Amarna Period was the closest to a schism, but this does not fit the mold, as the people continued to cling to their beliefs in spite of the Pharaoh's attempt to enforce a new religion. In fact, following his death, the people grew even closer to their deities, seeing future pharaohs as less important than direct worship. Greek and Roman invasions only added to the pantheons. It was only with the introduction of Judeo-Christian religions that the people finally surrendered their beliefs, but still not without exception. Isis is seen by many as an important angel in certain Islamic sects.
I would say that the Ancient Egyptians could be said to be non-schismatic.
