Most remodeling and cleanout debris is fine to load. What stays out is set by South Carolina law and by the county landfill.
South Carolina keeps used oil and lead-acid batteries out of regular trash. State law also bars computers, monitors, and TVs from waste headed to a landfill, and the landfill can turn away a load with more than a small amount of them. The Solid Waste Authority notes that state law bans yard waste from household trash landfills too.
Other items to leave out include hazardous waste, liquids, paint, solvents, fuel, and asbestos. Tires are accepted at the landfill for a much higher fee, so mention them when you book.
If you're unsure about something, ask your account manager before it goes in.