I am allergic to cats and want to buy a home that is owned by a cat owner, should I buy the home?

Yes. The house will need to be thoroughly cleaned before you move in. Remove all carpeting. Repaint walls and ceiling. Pre-painting wall preparation with tsp will remove any cat allergen clinging to walls & ceiling. Make sure the previous owners take the cat with them when they leave.
No problem. Just be sure to give the home a thorough cleaning before moving in. Clean all carpets and wipe down all surfaces including walls. Best that you hire someone. You wouldn't want the exposure.