People who are allergic to cats are actually allergic to certain proteins found in the animals' skin secretions and saliva; which particular proteins are responsible, however, varies from allergy sufferer to allergy sufferer. Since all cats shed skin and spread saliva around their environment, there is no such thing as a cat incapable of provoking allergic reactions, although it is common for a given cat to cause an allergic reaction in some -- but not all -- people who are allergic to cats.
Not all cats are identical with respect to the proteins contained in their skin secretions and saliva is most strongly supported by the information above.