Asbestos is a composite of long and fibrous silicate crystals, used especially for its resistance to heat, chemical reactions and electricity. As such, asbestos is required for certain armor modifications to resist fire damage, as well as modifying weapons that used fire, like the flamer, or need to be insulated from added heat, like the power fist or super sledge.
Asbestos was used well-throughout the 1950s before it was discovered that exposure to it caused cancer and other health problems. As a result, there was a mass removal of it from buildings and structures. Due to the nature of the Fallout series taking place in a Raygun Gothicretrofuturisticscience fiction this material was presented as both popular and safe.