Today I learned of the existence of "organic, wheat-based cat litter"
I was surprised when I walked into a pet store last week to see an aisle cap advertising a new tofu based cat litter.
Not sure if available in the American market, but I had good experiences with Cassava root based ones, though it is expensive.
Organic cat litters have the advantage the results can be composted.
They have the disadvantage that they don't control odor well, and when composted smell even worse. So don't try to compost them at home.