Its just as true of Eastern Christianity.
> the fact remains that Christianity has taken deep root in a number of places in the world that were free of western biases, e.g., China, Korea, Africa, and South America.
All of those examples are largely a consequence of imperialism (largely, on the part of societies comprising Western Christendom.)
That's not to say that there aren't a few cases of durable Christian communities in regions (IIRC, particularly in the Middle East and East Africa, and some in South Asia) where they aren't a result of the heritage of ties between the common ancestor of modern Roman Catholic, Protestant, and Orthodox Christianity and the Roman empire, including those descendant churches ties to imperialist European states, these isolated communities are notable as exceptions within Christianity.