Animals are domesticated but they still have instincts. Dogs can be trained, cats for the most part cannot. Small yip-yip dogs (puntables as a buddy of mine calls them) are usually no problem. Bigger dogs most times are friendly to the bird because it recognizes it as part of the family, like a baby. Cats however are not always so non-instinctual. There are many articles, videos and Facebook posts that tell the story about the cat and bird that lived together for 8 years and the cat then just attacked and killed the bird. Be weary of all animals with your bird but cats especially. Looney Tunes cartoons (Sylvester & Tweety) were based off of real observations. Either way, if you have a bird in the house with other animals, especially if their wings are clipped, keep the other pets at bay to get used to the bird. Teach them to only go onto certain perches and places in the house. When their wings grow back then they can be fully flighted and knowing their boundaries then the animals can interact a bit more but being fully flighted, this gives the bird the ability to avoid danger if it arises. You can’t be everywhere at once so giving the bird this ability to protect itself may save its life.
