Framing, drywall, stucco, flooring, roofing, cabinets, fixtures and ordinary cleanout debris are all normal loads. The exclusions come from California hazardous waste law and, more tightly here, from the recovery facility's own rejection list.
CalRecycle says plainly that hazardous waste cannot go in the garbage anywhere in California. That rules out paint, solvents and thinners, aerosol cans with product still in them, pesticides, pool chemicals, antifreeze, used oil and oil filters, propane and other gas cylinders, fluorescent tubes and batteries of every type. Electronics and tires are also barred from the trash statewide.
The facility that takes Bell Gardens loads goes further on three items that turn up on real demolition jobs. Treated wood waste is rejected. Non-hazardous material containing asbestos is rejected. Whole car, truck and motorcycle tires are rejected, as are liquid waste, used oil, sandblasting sand and fly ash. One rejected item can send a whole container back, so pull those out before loading and ask your account manager about anything you are not sure of.