I found that establishing missions can decrease natives' negative attitude against you. It decreases the "Your way of life is threatening us" (something like that)
My neighbour, the Sioux, has reached "Annoyed" stage. I have to appease Sitting Bull by presenting gifts until it reaches "Cautious".
I got 3 missionaries to establish missions in their settlements. That immediately went into "Pleased" stage.
However for some reason, Sitting Bull decided to go to war with me. It looks like the "Your way of life is threatening us" suddenly increases (that baffles me, but I guess it must have been the liberty bells at work).
Anyone has similar situation?