Yep, dogs can be allergic to cats. It sounds weird, because you may think that if they're allergic to cats then why aren't they allergic to themselves. But the reason for allergy is not, in fact, the fur of animals, it's the dead skin coming off. And cat's produce less of this 'dandruff' you might call it. That's why people tend to be more allergic to dogs than cats. And cats' skin is different from dogs', that's why dogs can be allergic to cats.