Lumber, drywall, roofing, flooring, cabinets, trim, doors, carpet, furniture, and ordinary cleanout junk are all fine in a roll-off.
Texas sets the outer boundary. The Texas Commission on Environmental Quality lists wastes barred from every municipal landfill in the state: lead-acid batteries, do-it-yourself used motor oil, used oil filters, whole scrap tires, refrigerators, freezers, air conditioners and anything else holding refrigerant, bulk liquid waste, anything with free liquids in it, regulated hazardous waste, PCB waste, and radioactive material.
Asbestos is treated as a special waste in Texas, and the state tells you to call the landfill before you move it, because many will not take it at all. Abatement belongs with a licensed contractor.
The local list is shorter but just as firm. The county transfer station will not take concrete, bricks, rocks or masonry units, and it also refuses oil and oil filters, brush, paint of any type, chemicals, and batteries. Those materials need a route arranged before loading day rather than after.
If an item on your list looks questionable, raise it with your account manager and we'll find the right place for it.