Not sure what you mean by that. I don't know how historically accurate the movie is, but as far as I know, the Portugese Catholic Church convinced these natives to convert to Christianity then turned their backs on them when coerced by the wealthy landowners and traders. It was they who attacked the natives, not the Church.The movie had several critical problems.
As for the music, you are close. I believe that the title(s) I was referring to are Gabrie's Oboe/The Waterfall from The Mission soundtrack. I borrowed the CD from the library once after hearing Yo Yo Ma play a version on the radio and I was captivated and those were the names given to the 2 tracks which just run into each other as if one tune. Here is Ennio himself conducting what I think is the best version of the music. You will hear the Vita Nostra part when the choir sings.