Thanks so much for all the replies! It's so confusing when I see so many videos on youtube with people having parrots and cats in the same room but its always seemed like an accident waiting to happen. I always cringe when I see many of them have their bird literally right next to the cat chewing on the cat's whiskers!
Seeing the replies here REALLY makes me no longer comfortable to even think about getting a kitten because I CANNOT imagine having to separate my birds into a separate room from my cat. It seems I must choose birds OR cat, but NOT both and of course ZERO chance I would EVER rehome my birds!! It confused me so much as an experienced avian contact told me it would be OK so long as I get the cat as a kitten and "train" them.
I was hoping to get a Moustache parakeet one day.... not anytime soon... this would be
many years from now. What size parrot do you feel is OK to have around a cat? If I had a Macaw or Cockatoo I'd be more fearful of the cat getting injured

I will never have a Macaw or Cockatoo however. So I guess I must choose if I want to have a Moustache parakeet or a cat many years from now. I cannot imagine not having a bird in my life though... hence why I wonder what size/type of parrot would you feel comfortable having a cat in the same house with?