Koreans have gotten massively christianized in the past few decades. Being American allies has done a number to to both Korea and Japan but has damaged the first more. They somehow took the worst aspects of both the native Korean culture and Christianity and combined it and made it worse. I'd say the everyday Americans are much more chilled out compared to Koreans when it comes to evangelising.
I'm sure you already know that India falls in what they call the 10-40 window. Basically they posit that most of the non-abrahamic people in the world to who 'the gospel hasn't reached yet' live between the 10°N to 40°N parallels. To them, this is their Alaskan gold rush, this is their Terra incognita, their manifest destiny opportunity. And if you recall, all of these involved denigrating and demonising the native populace to support their imperio-colonial belief.
The Koreans, who have thrown away their own culture must show Hindus, Buddhists etc as savages and uncivilized to make their choices seem better. Like all recent converts they are more zealous about their faith and proving to themselves that their choice was the correct one, but it's a while country trying to do it. This is why they send more missionaries to India, even more than the western countries.
A side note: it was us who used to send monks to these lands, specifically Hindu monks at first and then later, Buddhist monks. This is a bit of role reversal but it'll be back to how it was when we have enough economic clout.