If they refuse you pets, please dont be insulted: they truly have the wlefare of the cats or dogs in mind first. And of your own pets. If they say dog not good with cats, that is simply because the dog's kamma does not involve cats in her future life with adopters.
Kamma, the black pure bred shepherd a bit shy, would have been fine with cats at our house. They did not want me to adopt her. Instead, I got to know her in Mundy where she was walked. Truly, pet adoption is always for the better for everyone at city animal shleter.