Lumber, drywall, stucco, roofing, flooring, cabinets, fencing, furniture, and ordinary cleanout material are all fine to load. The limits come from California's rules for hazardous and universal waste and from what the county landfill will take at the gate.
California treats batteries, non-empty aerosol cans, electronics such as televisions and monitors, and mercury-containing items like thermostats and thermometers as universal waste, which has to be handled apart from landfill trash. Household hazardous waste is in the same group, and the Fink Road landfill states plainly that it does not accept it.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos never belong in a standard container.
The county adds its own conditions. Friable asbestos is refused outright, and non-friable asbestos needs an approval letter from the Stanislaus County Hazardous Materials division before it can be delivered. Treated wood waste is accepted only when the load carries a variance from the California Department of Toxic Substances Control, and appliances like refrigerators, washers, dryers, and water heaters should be pulled out first because they carry extra charges.
Anything you're unsure about is worth a quick question to your account manager before it goes in.