Say what!!! I would argue that this goes against teaching you about lifetime responsibilities.
The cats been there way longer than the girlfriend, and surely she can get antihistamines for when she is over.
Perhaps thorough hoovering and a hepa air filter in the rooms the gf spends the most time.
Plus keeping the cat out of places like your dad's bedroom would be a start.
I would ask to compromise this stage,
How old is the cat?