Suppose there was a world in which there were no plants, and with that no vines, fibers, or cotton and whatnot. There are animals that produce fur, in large abundance, and so that is a major source of clothing. However, a large portion of the world, and where a large percentage of the population lives, is a desert. Because of this, thick fur based clothing would not be suitable for the heat. Could animal skin function as a reliable source for clothing? Would something more extreme work, such as rocks/clay?
thick fur based clothing would not be suitable for the heat
Tuareg and many other desert living people wear woolen clothing, because wool provides a good isolation against both the hot of the day and chill of the night. Even camels and dromedaries, just to name a few desert animals, have a woolen coating.
You don't need to resort to anything more fancy.
People have made clothing for various climates from the hair of many animals (North American native tribes made felt from dog hair, for instance, Mongol yurts were originally covered with horse hair felt, and almost any domestic animal with longer hair than a Jersey cow or Arabian horse can offer useful hair).
As already noted, wool is good for both hot and cold -- it breathes, can be spun and woven very thin and the color left light for hot climates, yet can be spun and woven thick and heavy or felted for colder weather (like desert nights). Horsehair from manes and tails can be woven into stiff material that makes good light armor.
Beyond hair, of course there's leather -- it's usually considered too hot for desert sun, but it can be used as an over-layer, stiffened by boiling in wax or fat and formed to provide a parasol effect (like the broad hats Chinese railroad workers often wore in the American west). Tanning can be a little tricky without plant sources of tannin (oak, tea, etc.) but there are tanning methods that use byproducts from the slaughtered animal itself, or from another animal.
Beyond that yet, horn or hoof can be carved and heat-formed into shaping stays or struts, to help with keeping the leather away from skin (so cooling airflow can pass underneath while the leather keeps the sun off the body.
Your people cover their bodies with adherent materials - white clay, ash, sand, charcoal, and pigmented minerals. Sometimes they use a layer of grease and then sand or ash pressed atop that, periodically refreshed over the day. The body paint can decorate or camouflage as circumstances warrant. It can provide protection from sun and wind and insects. It traps dirt which then is easily removed. It smells like the herbs and aromatic resins that are added to it. It looks awesome.