Most cleanout and building debris is fine to load. What stays out is set by California's hazardous waste rules and by what the County sites accept.
California makes it illegal to throw hazardous waste in the trash. That covers all batteries, fluorescent bulbs and tubes, propane tanks, and aerosol cans that still hold chemicals. It also covers TVs, monitors, computers, and other electronics. Old fence posts and other treated wood must be handled as hazardous waste too. The full list is on the CalRecycle banned items page.
Standard exclusions apply as well: no liquids, paint, solvents, fuel, or asbestos. The County takes household hazardous waste through a separate program, which you can reach at 800-645-9228. Tires are handled per piece at County sites, so keep them separate.
If you're unsure about an item, ask your account manager before it goes in.