Most construction and cleanout debris is fine. Wood, drywall, shingles, flooring, cabinets, furniture, and household junk all go in without trouble.
The refusals here come from the regional transfer stations, and the list is specific. They cannot take asbestos-containing material, burned material or wildfire ash, flat or built-up roofing, loads of liquids, petroleum-contaminated soil, radioactive metals, electric vehicle batteries, or vehicles. Flat roofing is the surprise on that list, since ordinary shingle tear-off is accepted and flat roofing is not.
Asbestos deserves extra care. The transfer stations now ask every customer for documentation about asbestos, and anything left behind that needs testing or removal can be billed back. The regional government sets this out on its own transfer station page.
Hazardous waste, wet paint, solvents, fuel, propane tanks, pool chemicals, used oil, and batteries all stay out too, and Sherwood's own code bars hazardous waste from any collection container. When an item is borderline, ask your account manager first.