Terriers will chase anything that moves. Most other breeds of dog have been encouraged by their owners to chase cats. Many dogs and cats live together quite harmoniously. Cats are usually well able to stick up for themselves, and are usually far to quick for a dog to catch.
I have two terriers who live perfectly happily with cats. In fact they all chase each other on occasions. Quite honestly most domestic cats will happily live with dogs and dogs with cats. Cats very often dislike other cats more than they dislike dogs.
They don't hate each other. If a cat knows a dog they are the best of friends and the other way round.
cats can be very tolerent of dogs.
I have one that sits in my back garden and does but an eyelash when the dog comes out the back door at warp factor 5.
He just sits there watching him and when the dog goes in for a closer look he even returns the greeting.
Thats because the cat lives with two dogs and is used to them and their strange and nutty ways.
When my dog gave birth to a single puppy, I brought home an abandoned kitten just a few days old and she reared it until it was about six weeks. She fed and cleaned it and it played with the puppy. The mum however would chase any other cat that came into our garden although I had four of my own and she would sleep with them in their basket.