The problem with owning a cat and a bird at the same time is that it always seems that people either don't take the severe risk to the bird's life seriously, or they start-out taking it seriously and then they quickly start slacking. Or they are convinced that "their cat" is different than other cats, and they start taking chances and risks that eventually end-up in tragedy.
All cats, no matter the species, no matter their perceived temperament, no matter their past history of behavior around other animals are naturally predators to birds. Period. All cats have an innate instinct and predatory drive, and even a very friendly, docile, lazy house cat that has never been allowed outside and that has never shown any interest in birds still possesses this predatory drive and innate instinct to hunt, torture, and kill birds. It's just a fact of life. And as such, if you don't take this situation in your home seriously it will always end in tragedy and heartache. And you can't ever blame the cat for it when it happens, it's not their fault at all.
So, the answer is yes, it's possible to keep a bird and a cat in the same house, but ONLY if you keep them separated at all times. And here's another factor that no one ever thinks about, but the fact is that just like the cat is naturally a predator, birds are naturally prey. In-addition, birds can become extremely stressed very quickly, and when a bird becomes extremely stressed they can literally die from it. And many cat owners who also own a bird think it's perfectly alright to allow their cat to be in the same room as the bird, as long as the bird is locked inside their cage....This is just not true at all!!! Try to imagine how stressed a parrot must be when they are locked inside a cage, no way to get away, and they are constantly having to look at a cat staring at them all day long, watching a cat walk around past their cage all day long, or laying in front of their cage, etc. This isn't at all fair to the poor bird, it's basically psychological torture for them.
So the bottom-line is yes, you can have a cat and a bird in the same house, but only if you commit to keeping them totally and completely separate. And realize that your bird cannot be neglected because it's easier for the cat or more convenient for the cat. Meaning that any parrot you bring home, regardless of species, needs at least 4-5 hours of out-of-cage-time every single day to stay happy and healthy. So this means that the cat must be locked inside a separate room behind a latching door for at least 4-5 hours a day, or any time the bird is out of it's cage. So if you're not okay with doing that to your cat, then it's not wise to get a bird, because inevitably what will happen in the bird will end-up spending all their time locked inside a cage, and it's just not going to work. That's what creates pluckers. And you also cannot allow the cat to allowed to hang-out around the bird's cage at all, as this is going to incredibly stress-out the bird. So to make it work you have to figure out a way to keep the cat and the bird totally separated most of the time. And there is no such thing as "supervising the cat" when the bird is out, because it only takes a split-second to have a dead bird. Most birds that are attacked by cats don't die of the physical injuries they obtain from the attack, but rather from the severe stress of the attack.
***Something else that must be known by any cat owner thinking about getting a bird is that the saliva of any cat is toxic/poisonous to all birds, and the cat's saliva cannot come in contact with the bird at any time, as if they become infected with the bacteria that's present in the cat's saliva, most of the time they die, as even antibiotics usually don't work.