Use directly shoes could be not so practical and reproducible. I will try to find first to figure out which experiment could be more convincing. So why don't take many little piece of leather, cotton and synthetic fiber and make some general test (maybe useful even for clothes). These are what is passing through my mind.
Wettability and permeability
One of the most important thing is that substance drop over the shoes don't get in touch with the skin. So you could measure the contact angle of polar and non polar liquids over different "shoes textile" and find which has the lower one.
For permeability there are also some simple instrument you can buy.
Thermal conduction and inflammability
Even if this is more difficult to perform you could try to make your own system with a little hot plate and some thermocouples to see which materials do not conduct heat or is less flammable. One simple test could be the Clothes iron test (this in fact doesn't exist) you can palace a piece of different shoes textile and place it beneath the clothes iron measure the time at which it burns.
Acid and bases resistance
Why don't you put a little piece of textile over a piece of paper with an acid-base indicator and then put a known amount of acid or base over it if you do it in a glass table you can monitor when the acid reach the other side watching when the paper change color.
Pieces of broken glass could cut the textile so you could perform some test for determinate which textile is more hard to penetrate.