Ordinary household and construction debris is welcome. The real limits here come from Oregon Metro, the regional government that decides where greater Portland's waste may go and what its own sites will take.
Metro will not accept asbestos-containing material, burned material or wildfire ash, flat and built-up roofing, loads of liquids, petroleum-contaminated soil, radioactive metals, or electric vehicle batteries. Vehicles are out as well.
Asbestos is the one that catches remodelers off guard. Metro now requires asbestos documentation from every customer bringing construction debris, so popcorn ceilings, old vinyl flooring, pipe wrap, and siding on a pre-1990 house need testing before they go in. Metro warns that a customer who leaves untested material behind can be billed for testing and removal.
Hazardous waste, paint, solvents, fuel, used oil, pool chemicals, and batteries never belong in a standard container either.
Flat roofing deserves its own note, since torch-down and built-up roofing is common on Beaverton commercial buildings and Metro turns it away. Tell your account manager what roof you are pulling off and they will arrange the right destination for it.