Preheat the oven to 220˚F. Pour the pretzel twists, oyster crackers, and Rice Chex onto a large, rimmed sheet pan (or into a roasting pan) and stir to combine.
Whisk together the butter-flavored popcorn oil, Italian dressing mix, ranch dressing mix, garlic powder, onion powder, and cayenne pepper. Pour the mixture over the ingredients on the sheet pan and stir until well coated, scraping the excess off the bottom as you go.
Bake the snack mix for 20-25 minutes, stirring after 15 minutes, scraping the seasoning mixture off the bottom as needed.