Most construction and cleanout debris is fine. California's rules on hazardous household waste set the main limits.
The state bans many common items from the trash. The list includes fluorescent lamps, LED lights, batteries of all kinds, latex and oil-based paint, aerosol cans that aren't empty, solvents, pool chemicals, pesticides, antifreeze, motor oil and filters, propane cylinders, electronics, and mercury thermostats. Hazardous waste, liquids, fuel, and asbestos stay out of a standard dumpster too.
Two items often turn up on remodels here. Older siding, roofing, and cement board can contain asbestos. Treated wood, such as old fence posts, needs separate handling under state rules.
The Mojave-Rosamond Landfill itself turns away hazardous waste, hot ashes, and liquids of any kind. It does take tires, appliances, electronics, treated wood, and used motor oil as separate items, so pull them out of your container.
Ask your account manager about any item before you load it.