I had a siamese cat years ago when I had my societies. They were in a cage I built myself of 1/2" hardware cloth. The cat could climb up the side of the cage and lie on the top and look down at the birds. But because of the small guage wire she couldn't get her paws in. She would lay on top for hours though, watching them. I'd come home and find her face down on the cage top, sound asleep!
The societies were so laid back that they got used to her and pretty much ignored her, and even raised babies. As she got older and fatter, she found it harder to climb the cage. It was on a stand about 3 feet off the ground. She would sit in front of it, and then jump straight up, to peek at them when she heard them scrabbling around on the bottom of the cage. It must have looked funny to them, to see this head pop up and then drop out of site.
Maybe I was lucky, but no harm came to them or the cat. The only time I ever shut her away was when I was cleaning the cage, in case a bird slipped by my arm.
My current cat is 13, and she's too old and lazy to climb my cage, so is content to sit on the back of a chair and press her face up to the cage. The goldbreasts ignore her. They are more nervous of me than the cat. But again, this cage is not a store bought cage, with no gaps for escapes. So except for cleaning time, there is no way for the cat to open doors or get a paw in, or on the birds.
I think you will find that eventually, when they find they can't get in the cage, they will tire of the birds to some degree. But in any cage but the 1/2" square wire, I would definitely supervise when they are birdwatching!
bedroom smells "birdy" so I added an air purifier. It hasn't got rid of the smell much. I'm not sure I like it.
