It can cause disease in many other animals, including people. However many other animals can tolerate stronger antibiotics that can deal with it, but rabbits and guinea pigs can't
Actually itisn't that the antibiotics used in rabbits can't deal with it, usually it is that they can't reach it as tissue penetration varies depending on location. Penetration into the ear is very poor which is why ear infections are so hard to treat, the same goes for snuffles, the nasal passages are hard to get the drugs into without giving a dose that would kill the rabbit