What are the possible health concerns of purebred cats ?

The vet recommended hypoallergenic food for my sister's highly inbred British Shorthair because she was having bloody stools. Now her anxiety and brain issues seem better but she's still not normal and her stomach sags though she isn't fat.

It depends on the breed. Basically, in coming up with certain breeds of cats (and dogs too!), people have genetically altered these animals. This can cause other problems to arise. For example, I've had persian and himalyan cats that have problems with their nose and eyes because of how they've been bred to have flat faces (I actually just posted a question asking for help on this!!). But another issue too I think is all of the preservatives in the food we feed to animals now. But....just another opinion : )