If you could show hunter-gatherers a raindance that called on a different spirit and worked with perfect reliability, or, equivalently, a desalination plant, they'd probably chuck the old spirit right out the window.

There's no need to speculate--this has actually happened. From what I know of the current state of Native American culture (which is admittedly limited), modern science is fully accepted for practical purposes, and traditional beliefs guide when to party, how to mourn, how to celebrate rites of passage, etc.

The only people who seem to think science conflicts with Native American belief systems, are New Age converts coming from a Western religious background. From the linked article:

A Minnesota couple who refused chemotherapy for their 13-year-old son was ordered Friday to have the boy re-evaluated... Brown County District Judge John Rodenberg found Daniel Hauser has been "medically neglected" by his parents, Colleen and Anthony Hauser, who belong to a religious group that believes in using only natural healing methods practiced by some American Indians.