Parrots are ok in a community if they are the same size as their tank mates.
Smaller parrots would be picked on by fish such as Jacks or Midas etc, and a big parrot can make life hell for a smaller cichlid if it chooses to - so it's all about balance.
Another consideration is colouring. I have a red parrot and a yellow parrot, and the interaction with fish of the same colour is quite different from that with the darker fish in the tank.
It's an unpredictable arrangement in general, so give it a go and see how they get on - but size is important in this case
55 gal...
1 blue Mbuna - 1 zebra Mbuna - 3 blue Acara - 1 Electric blue Hap - 2 Blood Parrots - 3 Oscars - 1 Lima Shovel nose - 3 Sailfin Plecos - 1 Moorii - 3 yellow Severum - 3 striped Severum