So they don't really need the foot protection that many humans deem necessary. Furries are sensual beings, and the tactile sense of the soles transmits important impressions of the environment. Shoes would prevent this sense from working. You are nice to the world, so that the world is nice to you. The fur would make it uncomfortable to put on shoes, and it would probably be too warm for most furries to wear shoes on top of fur at the usual temperatures.
Furries use body language a lot.
In addition to handpaw gestures, facial expressions, movable ears and tail, footpaws can express a lot of emotions when bare. Furries enjoy having their paws in good tough natural shape rather than soft, weak and deformed by footwear. Furries are playful and enjoy being swift-footed rather than plodding around with a clunky shod walk. Speaking from an artist's perspective, footpaws give a good additional indication of species and personality. In a clothed anthropomorphic furry, the bare footpaws give a good visual counterweight to the exposed bodyparts further up.