Framing, drywall, stucco, roofing, flooring, cabinets, fixtures, furniture, and ordinary household junk are all fine. California, though, keeps more material out of the trash than most states do.
CalRecycle is blunt about it: putting hazardous waste in the garbage is against the law. Its banned list covers fluorescent tubes and LED lights, every type of battery, latex and oil-based paint, thinners, pool chemicals, pesticides, antifreeze, motor oil and filters, propane and other compressed gas cylinders, photo waste, and anything with mercury in it.
Two entries on that list catch remodelers off guard. Treated wood, the kind used for fences, decks, and sill plates, has to be handled as hazardous waste rather than tossed with clean lumber. Electronics of any kind, from a television down to a cordless phone, are also barred from the trash.
Asbestos, liquids, solvents, fuel, and tires stay out of a standard container as well. Tires are not hazardous, but the state keeps them out of landfills to prevent fires and standing water.
Sort the restricted items out before loading and tell your account manager what you found. One banned item can hold up an entire load at the gate.