Most debris from a cleanout or remodel is fine to load. California's rules on items banned from the trash set most of the limits.
CalRecycle lists fluorescent lamps and tubes, all batteries, latex and oil-based paint, partly full aerosol cans, pesticides, some pool chemicals, antifreeze, motor oil and filters, and propane tanks among the items that can't go in the trash. Tires are banned too, to prevent mosquito breeding and tire fires.
Two building materials come up often in remodels. Asbestos can be found in some older cement, roofing, flooring, and siding. Treated wood, including a lot of old fencing, must be handled as hazardous waste rather than thrown away.
Electronics such as TVs, monitors, laptops, and printers often contain hazardous parts, so they go to e-waste recycling instead.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster. If something on your list is uncertain, your account manager can check before it goes in.