Ordinary household and remodel debris is fine, within the construction limit covered below. The hard exclusions come from California rules and from the county landfill.
Under state law, hazardous waste, radioactive waste, and medical waste are not solid waste at all and cannot go to a landfill. Paint, solvents, fuel, used oil, and pool chemicals all fall on that side. Fresno County runs a household hazardous waste facility in Fresno for those, and your account manager can point you to it.
Reedley's own rules add a list that needs separate arrangements before disposal: ammunition, explosives, industrial waste, chemicals, acids, drugs and medicines, infectious waste, and anything too large or too heavy for collection equipment, like machine parts, large metal, logs, and tree stumps. Hot coals and ashes can never go into a container set out for collection.
Electronics and mattresses have free options for Reedley residents at a transfer station in nearby Kingsburg, and the City's solid waste page has the address. Tires are billed per piece at the county landfill rather than by weight.
One more local quirk worth knowing: pulling salvageable material back out of a container is against City rules for anyone but the franchise hauler, which matters on an unattended job site. If you are unsure about an item, ask your account manager before it goes in.