It would be simple to say nylon, but the truth is there are a variety of textiles fanny packs can be made from that lend themselves to different uses. There are even different types of nylon. For example, TPU-backed nylon creates a 100% waterproof pack that is ideal for fishing.
Also, consider the Monos Metro Sling, a pack available in either nylon or a vegan leather option as well as the Cotopaxi Bataan, a fanny pack made from 100% repurposed nylon.