I assume the shell/structure of a solid rocket booster requires protection from the ~3000°C+ combustion temperature of its fuel.
What does/did NASA, Roscosmos, SpaceX, Ariane 5, etc use to line their booster rockets with a refractory material, and how thick is/was that material?
The shuttle SRBs didn't have refractory material as such; they were lined with an impregnated rubber insulation.
The insulation was
made of chrysotile-filled rubber: chrysotile being the most-common mineral form of asbestos.
source: https://www.nasaspaceflight.com/2014/09/atk-making-progress-srb-propellant-void-issue/
(Asbestos by itself would be considered a refractory material)
The thickness of the insulation varied somewhat, in this picture you can see a representative thickness of 1.81 inches (labeled NBR Insulation).
Image source: https://history.nasa.gov/rogersrep/v2l59.htm
The nozzle lining was designed to ablate away, you can read about that in this answer: https://space.stackexchange.com/a/22004/6944
