Ordinary remodel and cleanout debris is fine. The limits come from California's hazardous waste rules, which apply everywhere in the state, plus what the receiving landfill turns away at the gate.
California bans a long list of household items from the trash, and the state's waste banned from the trash page is the one to check before you load. Paint of any kind, solvents and thinners, pesticides, pool chemicals, motor oil, antifreeze, and non-empty aerosol cans all have to go elsewhere. So do every type of battery, fluorescent tubes, LED bulbs, and propane cylinders. Asbestos is banned outright, and treated wood with preservatives in it has to be handled as hazardous waste rather than lumber.
Electronics are a separate problem. Televisions, monitors, computers, printers, microwaves, and phones are all barred, and the landfill requires that electronics, appliances, and household hazardous material be dealt with before a vehicle enters the tipping area. Tires are banned as well, for mosquito and fire reasons rather than chemical ones.
Liquids, fuel, and pressurized cylinders never belong in a roll-off container regardless of the project. If you are holding something and cannot tell which pile it goes in, send a photo to your account manager and ask first.