This is a complex and interesting question, about which there is much misunderstanding even among scholars and Sangha.
I researched this at length while writing Sects & Sectarianism. Among my conclusions:
- There is a formal definition of “schism” in the Vinaya. To fulfill this legal definition, one must hold a separate recitation of Patimokkha with the intention of creating a schism and harming Buddhism.
- To my knowledge, this has never happened. I believe the reason is that when Devadatta did it, the Buddha said he’ll go to hell. I don’t think anyone wants to test out whether the Buddha was being literal or not!
- The evidence attests that existing schools of Buddhism arose primarily due to geographical separation, secondly due to doctrinal differences, and thirdly due to Vinaya interpretations. These schools were separated to a degree, but not schismatic in the technical sense.
- In reality, personal differences or competition for resources likely played a part.
- Modern-day Sangha are descended from three of the early scools: Theravada, Dharmaguptaka (east Asia), and Mulasarvastivada (central Asia). There is no evidence that these three schools were ever schismatic.
- Within each of these major schools there are several smaller groups. Typically one finds a few different “nikayas” within a country. For example, Thailand has the Maha Nikaya and the Dhammayuttika Nikaya. Sri Lanka has the Siam Nikaya (technically the same as the Maha Nikaya), Ramañña, and Amarapura. These for the most part perform Sanghakamma separately, but there is no real evidence that they are technically schismatic.
- The variety of modern schools seem to have arisen in the 19th century as a means to purify the Sangha against perceived or real corruption. They did so by invoking the semi-mythical purity of the “Kalyani Sima” in Myanmar, through which it was supposedly possible to connect to an unbroken lineage from the old Mahavihara in Sri Lanka. The modern Dhammayuttika, Amarapura, and Ramañña nikayas were formed in this way.
- The Siam/Maha Nikaya seems to not have been a school in the same sense, but merely whatever the tradition of the unreformed monks in Thailand happened to have been. Given the complxity of movement of Buddhism throughout history, it seems almost certain that this is a mix of different schools not representing a single lineage. However, it likely includes the Mulasarvastivada as well as the Sri Lanka Theravada.
- Again, within the recognized nikayas there are smaller groups who will not perform sanghakamma with each other. The monks of the Ajahn Chah tradition, for example, famously expelled the monks who performed bhikkhuni ordination and will no longer perform Sanghakamma with us.
- Finally, there are many monastics, including myself, who believe that all this is rather a waste of time. We are all sons and daughters of the Buddha and should love and accept each other.
It is hard to let go when your brothers and sisters are locked in conflict. We care about the Sangha, and it’s upsetting to see it treated this way. But yes, ultimately if the crisis cannot be resolved, then like the Buddha at Kosambi, one has to simply leave it behind and walk away.