Framing, drywall, roofing, siding, flooring, cabinets, furniture, and ordinary cleanout junk are all fine in a Mukilteo container. The limits come from Washington's rules on dangerous waste and from what the county will take at the scale.
Washington treats dangerous waste and moderate risk waste as separate streams from ordinary garbage, and the county transfer stations will not accept either one. That keeps paint, solvents, fuel, motor oil, pesticides, pool chemicals, propane cylinders, and any free liquid out of your container. Asbestos is handled under its own rules and never rides in a mixed load.
Yard waste and clean wood debris are also turned away at the three county transfer stations, which send those materials elsewhere. If your job mixes brush or clean cedar with construction debris, say so when you book so the load is routed correctly.
The county also refuses rodent-infested loads outright, and its recycling area serves residential customers only. Tires, mattresses, and appliances with cooling units need to be declared when you order rather than slipped into the container.
Anything you are unsure about is worth a quick question to your account manager before it goes in.