History has St. Thomas going to India spreading the gospel message. Similar to the church in the West, they are not all homogeneous. There are different organizations/grouping, and I'm not the expert on this at all so I won't try to give a history lesson based on my quick readings.
What I want to say is this. It seems there was a line drawn in the sand around some theory made by Nestorius. The church of the West agreed Nestorius was a heretic. The church in the East was more accepting of Nestorius.
It seems like it was a big thing. People who supported Nestorius actually moved outside the Roman Empire into Persia where Christians were being persecuted. Was the persecution from the Roman Church worse than the persecution they got from non-Christians?
So what was the issue with Nestorius' theory:
Nestorius' teachings became the root of controversy when he publicly challenged usage of the long-used title Theotokos (Mother of God) for the Virgin Mary. He suggested that the title denied Christ's full humanity, arguing instead that Jesus had two loosely joined natures, the divine Logos and the human Jesus. As such he proposed Christotokos (Mother of Christ) as a more suitable title for Mary.http://en.wikipedia.org/wiki/Nestorianism#Nestorian_doctrine
I must be missing something. This doesn't seem like Nestorius was questioning any essential belief here. He believed Jesus was both divine and human. He thought the title 'Mother of God' was a bit strong for a human.
We sure do have a history of making mountains out of molehills.