My understanding is that a number of different protestant denominations, including the Anglican Church in India, the Presbyterian Church in India, and the Methodist church in India, combined into united north and south Indian churches. Why was this ecumenical unification successful in India, when it has not happened in the United States or Europe (at least, not as broadly)?
The situation in India, as with Indonesia, is largely a result of the colonial empire of the Calvinist Dutch Republic, beginning in 1602 with the Dutch East India Company (VOC). The Catholic Portuguese had already established trade relationships with indigenous kingdoms and sultanates from Goa, Malabar, Malacca, all the way through the Malukus in the previous century. Although the Portuguese had introduced Catholicism, it failed to remain in effect after the Dutch conquered the Portuguese little by little in what was then known as the East Indies.
The Dutch VOC imported Calvinist missionaries to convert both the non-Christian indigenous peoples, as well as the already Catholic locals and former Portuguese officials who remained after the steady conquest. The Dutch were hostile to the Portuguese for various reasons, not only because of the threat to mercantile dominance in the region posed by their Catholic merchants, but also because the Dutch Republic was at war with Hapsburg Spain, which at various times also possessed parts of the Low Countries, Portugal, Spain, Austria, and other important holdings including all of the overseas territories of the aforementioned sovereign states. The Portuguese represented the greatest threat to the Dutch Republic, not only in Asia but at home.
The Dutch Calvinists violently purged Catholics, Mennonites, and other Protestants out of the Republic, and the uniform exclusion of Catholics in Southeast Asia was no different, albeit with a more colonial and eventually imperial tone. A result of this purge and Protestant assertion of dominance is the current situation of a relatively unified church in India.
Hi--My parents immigrated from India to the U.S. in the 1980s, and I am a member of the CSI diaspora church in North America, so I may be able to answer your questions. A good resource on this question btw is The Reunion of the Church, by Lesslie Newbigin. Newbigin was a Reformed missionary from Britain who ended up being one of the first Bishops of the united Church, as well a famous author in the West upon his return.
Christianity in India, particularly in the state now known as Kerala, had existed for a long time. The tradition is that it had existed since St. Thomas had traveled to southern India and founded a Christian community there. This claim has typically been received skeptically in the West, but it is key to the identity of many Kerala Christians. I certainly buy into the belief as a matter of faith, and the traditions passed down in my family. At any rate, this "St. Thomas" Christian community's connections to the broader Christian world was cut off with the fall of the Roman Empire and the disestablishment of regular trade routes. Over the centuries those connections were reestablished, however fitfully.
Again, much of this relies on the Kerala Christian tradition that has been passed on to me, and I am not a historical scholar. But at some point the St. Thomas Christian community was in association with the Antioch church. This association became complicated with the arrival of the Europeans--particularly the Portuguese, who brought with them Roman Catholicism. The St. Thomas community began to be influenced by Catholic beliefs--there are varying accounts, but at some point schism did happen.
In the 1800s, British missionaries began to come to southern India, following the mercantile activities of the British East India Company. When they came to Kerala, they found a small existing St. Thomas Christian community. There was also Catholic activity, but many of the British missionaries were Protestant--Anglican, Methodist, Presbyterian, and Congregationalist (closely related to the Puritans).
These missionaries, from different denominations, realized that the mission field in India was so vast that they did not want to "waste" their efforts preaching in the same areas. They did not want simply to be poaching Methodists to their Anglican church. Instead, for the sake of preaching the Gospel widely, they divided India into districts--the Methodists would preach here, the Reformed would preach here, the Anglicans would preach here, etc. In this way, the hope was that every area of India would have one Protestant church to go to.
Over time, the Indians would move from one district to another. This meant that a Methodist from one village may not have a Methodist church in the other village--there's only an Anglican church there. For this reason, members of these churches would have letters showing them to be members of good standing in their home church, and would therefore be accepted by the sister mission church. Now I'm simplifying a lot here, but this was the basic upshot.
As this practice continued, and as the clergy and leadership of the Indian churches became "nativized" and less British, there emerged a stronger desire for unity among the mission churches. This led to a lot of dialogue, beginning in earnest in the 1900s and leading to an emergent union. These slow moves to union finally crested around the time of Indian independence, and the Church of South India and the Church of North India were officially created.
This movement has not yet happened elsewhere, but it is my hope (and the hope of my church) that all churches will continue to take visible steps toward unity for the sake of the Gospel. Such work will always be slow given theological differences and cultural blinders, but I earnestly believe it is in keeping with Christ's prayer in John 17, "that they all may be one." Hope this helps answer your question.