Everyday Hurst construction and household debris is accepted. The limits come from what the receiving site is allowed to take.
Hazardous waste stays out, and that covers paint, solvents, fuel, used oil, pesticides, pool chemicals, and anything corrosive. Liquids are out. Asbestos is out. Medical waste is out.
Hurst's own waste rules go further than most, because the City defines unacceptable waste by reference to what the receiving landfill may not accept, and it names tires, concrete, and bulk petroleum or chemical products in that list, along with sludge and refrigeration appliances that have not had their refrigerant removed by a certified technician. Concrete appearing on that list matters: a clean concrete load needs its own arrangement rather than a place in a mixed container, so say so when you book.
The City will not take brick or concrete at the curb either, and it does not collect old tires curbside at all. Both are reasons a container with a confirmed destination is the cleaner route on a demolition job.
Anything you are unsure about is worth a question to your account manager before it goes in.