While these items may drop for any class, they will never roll stats and skill bonuses that are intended to be used by other classes. Smart Loot never creates items intended for another class. Even enchanting cannot make a class-specific item roll stats that are not intended for the respective class.
Note that while some item types are technically not class-specific, they are of little to no use to classes other than those they are meant for; such as Bows being primarily intended for Amazons and Demon Hunters, yet most other classes can wield them too.
In Diablo III, most class-specific items can be transmogrified into their non-class-specific counterparts (such as Ceremonial Knives to Daggers), and vice versa, but only for classes that can use them.
Kadala has a chance to make any selected item roll either a generic type or a class-specific variant for the player's class, if such a variant exists.
In addition, in the third game, many class sets can only be equipped by one class, and most set bonuses have no effect on other classes. Kanai's Cube can extract essences from class-specific items, but may not grant their effects to characters of other classes.