Most debris from a remodel or cleanout is fine to load. The limits come from Alabama's rules and from the facility that takes your load.
Alabama keeps tight control of scrap tires. The Alabama Department of Environmental Management approves only certain landfills to accept them, so tires can't be tossed in with a mixed load. The same agency requires a waste review before hazardous or special waste can go to a landfill.
That means hazardous waste, liquids, paint, solvents, fuel, and asbestos stay out of a standard dumpster. Car batteries, propane tanks, and pressurized cans belong somewhere else too.
Local sites add their own limits. Jefferson County notes that Johns Transfer Station in Bessemer doesn't accept paint, batteries, or tires. For household chemicals and electronics, the county holds free drop-off events for residents a few times a year.
When you're not sure about an item, ask your account manager before it goes in the container.