I think that you need to read up on your rights as a renter and pet owner. This is an interesting site that is worth reading.
Renters Rights for Pet Owners | I Love Dogs Blog
I would fight it and if that didn't work I would look for another place to live. It appears that you have been living in the same place for years. Why does the landlord have a problem now? Seems to me that you wouldn't lose if you ended up in court. Good luck and don't let them push you around. Kitties are family members.