Riverside County's landfills do not accept hazardous waste in any form, and the county routes household and business hazardous material to separate facilities. That covers paint, solvents, fuel, used oil, pesticides, pool chemicals, and batteries, none of which belong in a rented container.
Asbestos is out, and so are liquids of any kind, pressurized cylinders, and medical sharps. Electronics, tires, and large appliances need to be set aside and named at booking, because each carries its own handling route and its own charge.
Jurupa Valley adds a definitional point that is useful rather than restrictive. The city treats large concrete and asphalt chunks and tree stumps as bulky waste, and says bulky waste is collected only during annual cleanups or by contractual arrangement with a permitted operator. In plain terms, a slab tear-out or a stump removal is a booked container job, not something to set at the curb.
The city also bars delivering any load to a site that is not a fully permitted, properly zoned solid waste facility, so where your debris ends up is a regulated choice rather than a convenient one. Ask your account manager about anything unusual before it is loaded.