Allergy to cats isn't an all-or-nothing thing; I know someone who's allergic to basically all cats other than her own, and actually I seem to be horribly allergic to the cat at the pub The Empress even though I've never been allergic to any others.

Also, installing air filtration systems because you're allergic to cats and dogs would surely be implausibly overcautious if there weren't actually any cats or dogs in the house...

Peter