Most building debris and household junk is welcome. The limits here come mainly from California's statewide list of material kept out of the trash.
The state is blunt about it: putting hazardous waste in the garbage, down a storm drain, or on the ground is illegal in California. The list of items banned from the trash is longer than most people expect. It includes all batteries, fluorescent tubes and LED lights, motor oil and filters, antifreeze, pesticides, oil-based paint, pool chemicals, and tires, which are barred to prevent mosquito breeding and tire fires.
Two of those matter a lot on a construction job. Asbestos in older cement board, roofing, flooring, and siding cannot go in a container, and neither can treated wood, which turns up as old fence posts, deck boards, and sill plates. Both need their own handling. Electronics are also out: the state treats televisions, monitors, computers, and similar gear as universal waste that cannot be put in household trash or buried in a landfill.
Beyond that, keep out liquids, solvents, fuel, and anything explosive or reactive. Yuba City's own rules add ammunition, chemicals, acids, medicines, and oversize items such as machine parts, logs, and tree stumps that can damage collection equipment. Large appliances and furniture are handled separately from regular trash in the city rules, so flag them when you book.
When something is borderline, ask your account manager before it goes in the container.