Green Grass, Running Water seeks to show the ways in which Native American spirituality and white culture clash and how the white culture forces itself on the Native traditions. It also shows how some of the traditions of both groups are rooted in similar mythology.
There are three ways that Thomas King shows this in the novel. The first is in the interactions between the Native and white religious figures. In the vignette between Jesus and Old Woman, he needs her help to calm the waves and save the people in peril. This shows a similar type of tradition—someone with the power to calm the water and the desire to save the people.
Next, there are interactions between the Native mythological figures and figures from white popular culture. Each of these popular culture figures has a negative impact on Native populations. Thomas King rewrites the stories with his mythological figures inserted into them and then twists it so that there's a positive outcome for the Native people. For example, John Wayne finds himself defeated by the Native Americans instead of the other way around.
Finally, Thomas King shows how white culture disrespects and disregards Native culture through the interactions between the two. For example, Amos is arrested when he and his family are stopped at the border on their way to perform a sacred tribal dance. Their costumes are confiscated and damaged. There is no respect for the Native culture shown by the white characters.