Most remodeling, roofing, and cleanout debris is fine for your dumpster. The limits come from state hazardous waste rules and from the county landfill.
Montana is unusual. The Montana Department of Environmental Quality says the state has no law banning electronics from landfills, and it hasn't banned other materials either. That doesn't mean anything goes. Hazardous waste must go to a permitted hazardous waste facility, and the landfill screens loads for it.
So keep hazardous waste, liquids, paint, solvents, fuel, propane tanks, and asbestos out of your container. The county holds a free household hazardous waste collection on the third Saturday of each month, by appointment, for items like oil-based paint, cleaners, and pesticides.
Tires, stoves, washers, dryers, and water heaters are taken at the landfill but handled apart from other trash. Refrigerators go in their own pile with the doors removed. Mention these items when you book.
Ask your account manager about anything you're unsure of before it goes in.