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.