To the extent the wearer notices?
Yes, they do. They get infected with fungus, which I imagine you would notice if your feet got infected, and they get infected with bacteria- especially cheap plastic kids’ shoes that don’t let air in and out. That’s why boys’ shoes often smell bad.
So which material reduces this effect the most?
Bacteria and fungus both prefer hot and humid environments. Anything that helps the shoe stay cool or dry will help, which is why most shoes have patterns of holes punched in the sides or toes, or use some kind of a breathable fabric in a low-wear area of the shoe.
Foot odor is actually not so much the feet, but the bacteria that grow on/around the feet.
Shoes can not get infected with microbes because shoes are not alive. You can’t infect non-living objects.
Shoes can certainly harbour microbes, and you can detect that easily through smell, but they can not possibly become infected.
Estrogen, apparently. Based on that last sentence about boys’ shoes.
P.S. Girls’ shoes can smell equally bad, if they are sneakers worn during strenuous athletics.
Equally bad? Not that there’s any way to test the strength of one odor vs. another, but it’s a fact that men sweat more than women do.
And more sweat = more food for bacteria, and thereby more stench.
Socks
Sodium bicarbonate - baking soda. And zinc powder.