It seems amazing the variety of peoples experiences with these fish. I have kept both CAEs and SAEs for many years. This is what I have found:
Only SAEs will eat hair algae (and they will do so all of their life, providing there is no other food source that is more tasty and easier to eat, like flakes). CAEs will not ever eat hair algae not even when they are small. CAEs can become agressive toward conspecies as well as flat bodied fish they can attach themselves to and eat the slime coat off of. SAEs will not become agressive against fish of their own kind. They like each others company like otos do. I have never seen them getting agressive and I have had several groups of them in numerous tanks. Anyone that will tell you that theirs did, probably ended up with Flying Foxes and not SAEs. A 30 gal is a bare minimum for 2 SAEs as they are active swimmers, but they will survive in a tank that size.
Your parrot fish might be ok if they are fast. I never had any so I can't judge them well enough but they are large bodied fish. The CAEs may see them as a target but then again they may not. Something you need to watch for when you move the CAEs to the parrots tank.
20g L46/hastatus/pygmy corys, 10g OEBTs, 10g blue bees/blue velvet shrimp, 10g CRS, 15g L174s, 10g yellow shrimp, 15g clown plecos/L340 fry, 25g L134s/CPDs, 29g Weitzmani/panda corys, 46g L134s/salt and pepper corys/BNs, rubberlip pleco, 55g SAE/L201s/L199s/BNs/kissing gourami, 75g L316s/BNs/old fish folk, 30g L340s/L211s/CPDs/micro rasboras,10g tangerine tiger/snowball shrimp, 20g L134/habrosus corys, 10g CPD fry