Primarily with the shrine offerings. title phrased like that in case there are other menus like that.
I dont have very good memory, so I remember that the shrines like either food, materials, or cloth, but not which for which. (person statue, stone pyramid, metal half moon. I think). I think the quality of the offering might increase the reward, but I dont know it for sure.
what I'm imagining is colouring options green/red based on previous interactions. if you've given a thing cloth and it didn't like it, cloth would be coloured red the next time you visit the same shrine.
I dont know how easy it would be to implement. I might have a go at modding later.