Most remodeling and cleanout debris is fine. The limits come from Virginia's rules for landfills and from what the Ivy transfer station will take.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster. The same goes for anything hot or smoldering, which the Ivy site asks customers not to bring.
A few items need special handling. Ivy charges extra for each appliance that holds Freon, like a refrigerator or window air conditioner. Tires are billed by the piece, so keep them out of the load or mention them when you book. Clean dirt, concrete, and asphalt cost far less to dispose of, but only when they're free of trash, rebar, and wood.
Leftover paint in its original can can go to Ivy on its own, any day it's open. Thinners, solvents, and glues are saved for the Rivanna Solid Waste Authority's household hazardous waste days.
Not sure about an item? Ask your account manager before you toss it.