Most construction and cleanout debris is fine. The specific limits here come from the county authority and they are unusually detailed.
Hazardous material is out everywhere: paint, solvents, fuel, used oil, pool chemicals, pesticides, and anything corrosive or flammable. The village groups asbestos, whole tires, used oil, lead-acid batteries, and biohazardous waste together as special waste, and its own collector is not required to take any of it.
Tires are not accepted at a county transfer station at all and carry a high per-ton rate at the landfill, so they need separate handling.
The county's biggest restriction is about which site takes your load, not about banning the material. A county transfer station cannot accept concrete, block, brick, tile, steel, rebar, roofing material, construction lumber, trusses, pallets, dirt, fill, sod, or large stumps, and the county says loads with more than a small quantity of those will be rejected. The landfill takes all of it. That is a routing problem rather than a loading problem, and it is handled for you.
Appliances, electronics, and anything unusual should be mentioned when you book. Ask your account manager if you are unsure about an item.