Lumber, drywall, plaster, stucco, roofing, flooring, cabinets, fixtures, furniture, and general cleanout debris are all fine. The hard limits come from California's statewide list.
CalRecycle keeps hazardous material out of the garbage across the state, and its wording is blunt: disposing of hazardous waste in the garbage, down storm drains, or onto the ground is illegal. The list covers paint of both kinds, solvents, pesticides, pool chemicals, acids and oxidizers, antifreeze, motor oil and filters, every type of battery, and all lamps and LED lights. Propane tanks and other compressed gas cylinders are out. Tires are banned as well, for mosquito and fire reasons rather than toxicity.
Two items catch Westside remodels in particular. Asbestos sits in older cement, roofing, flooring, and siding, which covers a great deal of pre-1980 Santa Monica housing stock, and it needs a licensed abatement contractor. Treated wood, the preserved lumber used in decks, fences, and planters, has to be managed as hazardous waste in California and cannot ride in a standard container.
No Santa Monica-specific banned list sits on top of the state one. The local constraint is about destination instead: debris has to reach an approved facility, and inert loads have to reach an approved inert site. Mention anything unusual to your account manager when you book and the right disposal route gets arranged with it.