It is generally recommended that rabbits should not be fed any kind of fungus like mushrooms or toadstools. Various sources state that shop-bought white button mushrooms are toxic to rabbits, but I am not aware of the specific reason other than a study in mice, which could have very different results. Identification of wild mushrooms (the spore-bearing fruiting body of a fungus) is notoriously difficult, and many wild mushrooms are poisonous to humans. Given that many foods that we eat are toxic to rabbits, it would seem sensible to not allow rabbits to eat any mushrooms. At the very least, unsuitable mushrooms could be hallucinogenic or cause diarrhea.