I brought a kitten to a house where there were already 2 pit bulls (byb bred ones) one of which enjoyed a fight although he didn't look for them. The cat was fine.
Later, I brought rottweiler puppies into a house with grown cats. They slapped the puppy around a little to teach it who was boss, and that was it.
I also brought an adult Airedale terrier to the same house with cats, and everyone was fine.
Bully breeds? Bully owners! Any dog is friendly, especially if you get a puppy. If you get a rescue, I agree with clm's diagnosis