Camels can eat cactus with thorns, because their mouth is lined with papillae, nodules that create a rough structure that helps them chew, It is the same tough fibrous protein that makes up hair, fingernails, snake scales, beaks, horns, hooves, etc.
This adaptation allows these desert specialists to eat what little vegetation is provided by the hot environment they are accustomed to.
It does hurt a camel to eat a thorny cactus, but they have adapted well to make it bearable