Most building and cleanout debris is fine to load. The limits come from California's rules on hazardous material and from what the county facility accepts.
California makes it illegal to put hazardous waste in the trash. That list covers all batteries, fluorescent tubes and LED bulbs, latex and oil-based paint, solvents, pesticides and herbicides, antifreeze, motor oil and filters, pool chemicals, and non-empty aerosol cans. Tires are banned as well, mostly to prevent mosquito breeding and tire fires.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster either. Treated wood, which shows up in old fencing and decks, has to be handled as hazardous waste, and propane tanks and other compressed gas cylinders need separate disposal.
The county facility also turns away hot ashes, liquids, and unprocessed auto bodies, and it checks loads at the gate. When something is questionable, ask your account manager before it goes in.