Most debris from a remodel or cleanout can go in. The limits come from Wyoming's disposal rules and from the landfill's own rules.
The Wyoming Department of Environmental Quality says all solid waste must go to a facility approved by both the state and the local government where it sits. In practice, that means the district landfill decides what it will take and how.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster. The landfill takes some of these items only under special rules. Friable asbestos needs a permit from the landfill manager, special paperwork, and a sealed steel drum. Paint, batteries, used oil, and antifreeze are accepted free from in-district residents, but only when brought in separately.
Tires need care too. They must come off the rims, they're charged per tire, and the landfill won't take them from outside the district. Keep tires out of your container and mention them when you book.
Your account manager can check any item you're unsure of before it goes in.