Lumber, drywall, roofing, siding, flooring, cabinets, fencing, furniture, and ordinary household debris all go in without issue. The limits come from North Carolina's disposal bans and from the County's own gate rules.
North Carolina has banned lead acid batteries from ordinary waste disposal since 1991, and a statewide ban on lithium-ion batteries at household waste sites takes effect on the first of December. Wake County asks that terminals be taped or each battery bagged separately and dropped at a household hazardous waste site instead. One loose power tool battery in a container is a genuine problem, not a technicality, because of the fire risk in a packed load.
Hazardous waste stays out in every case: paint, solvents, fuel, motor oil, pesticides, pool chemicals, asbestos, liquids, and sealed drums.
Tires need their own handling, and North Carolina requires a scrap tire form once there are five or more in a load. The County's neighborhood sites take no concrete or pavers at all, and they limit construction debris to homeowner waste, so a contractor's load belongs in a container headed for the landfill rather than at a drop-off site. When something has you unsure, ask your account manager before it goes in the container.