Nearly all Hurricane construction and household debris is accepted. The limits come from Utah's rules and from the county landfill.
Hazardous waste stays out, which covers paint, solvents, fuel, used oil, pesticides, pool chemicals, and anything corrosive. Liquids and asbestos are both out of a Hurricane container. Utah also bars lead acid batteries from any public solid waste facility, so car and equipment batteries have to be handled separately.
The City's own rule points the same way. It requires all solid waste generated inside the city to go to the county landfill, with hazardous waste, lead acid batteries and used oil expressly carved out and sent elsewhere. Those three are the clearest signal of what should never be loaded.
Tires need their own arrangement. The county limits how many it takes from a resident at one time and has stopped accepting them from businesses altogether, so a tire pile is a separate job rather than part of a container load.
If something in the pile has you guessing, ask your account manager before it goes in the container.