Framing, drywall, roofing, flooring, cabinets, fencing, furniture, and general cleanout junk are all fine. The limits come from California's list of material banned from the trash and from the gate rules at the receiving site.
California keeps hazardous material out of the garbage altogether. CalRecycle puts paint, solvents, pesticides, pool chemicals, antifreeze, motor oil, batteries of every type, fluorescent and LED lamps, propane cylinders, and all electronics on that list, so televisions, monitors, computers, and microwaves have to go to an electronic waste drop-off.
Two items catch remodels in this part of the county. Treated wood, the preserved lumber used for fences, planters, and sill plates, counts as hazardous waste in California and cannot ride in a standard container. Tires are not hazardous but they are banned from the trash and need separate handling with a fee of their own.
Liquids in any form, sealed drums, hot ashes, and medical waste are out as well, and asbestos has to be handled under its own rules before any demolition debris leaves the site. Los Angeles County runs a free household hazardous and electronic waste program for the material that cannot go in a container. If an item leaves you guessing, ask your account manager before it is loaded.