Normal building and household debris is welcome. California's rules on hazardous material are what set the limits, and a few of them catch people out on home projects.
The state's banned from the trash list keeps out paint of any kind, solvents, thinners, aerosol cans that are not empty, pesticides, pool chemicals, motor oil and filters, antifreeze, batteries of every type, fluorescent tubes and LED lamps, propane tanks and other pressurized cylinders, and all electronics, including televisions, monitors, computers, printers, and microwaves. Asbestos in older roofing, siding, or flooring is out as well.
Two more deserve a flag on a North County remodel. Pressure-treated lumber counts as hazardous waste in California, so old decking, fence posts, and landscape timbers cannot ride along with the rest of the debris. Tires are also barred from the trash, even though they are not hazardous.
City rules add the obvious ones: no needles, no infectious waste, no caustics or acids, and nothing flammable or explosive in a container.
Everything else, from drywall and framing to roofing, flooring, cabinets, and furniture, is fine. If an item is borderline, ask your account manager before it goes in.