Dogs are generally more accepting to a new cat. The dog may bark and chase outdoor cats that walk through their yard or cross their path however if you pick up that cat and bring the cat indoors then the dogs attitude is usually “if the cat is okay with my master then it is okay with me.”
It is an adjustment for the cat especially if the cat is feral or not accustomed to being around a dog. Cats usually need to bond with the dog before they will be able to reside under one roof.
The dog is fine with the cats but when the cat hisses at the dog the dog will bark at the cat.
When it comes to feral cats living with dogs it is best for the human to bond with the cat before they introduce the family dog. The reason I say this is because the cat will bond with the dog and will ignore the human.
When the cat walks past the dog and rubs his body or tail on the dog, it is a sign that the cat has bonded with the dog. My dog reacts to the cat bonding as a sign that it is time to nuzzle the cat with his nose and to be affectionate; my dog will lie down close to the cat and rest with the cat or take a nap.