In one chapter of the manga it's shown Tomura Shigaraki can disintegrate things with his feet. The disintegration activates apparently in the same way as the hands, when the 5 toes are in contact with the object. How does Tomura Shigaraki for not disintegrating his shoes then?
This is purely speculation, but socks with holes in them.
Shigaraki's power only triggers if he touches the target with all five fingers/toes on one hand/foot.
So he could have special socks with holes for one or more toes. Some toes touch the shoe, the others the sock, so neither decays.