Hello. Congrats on the new additions. I too have a Rainbow Shark (RBS) in with my Bloody Parrots. My Parrots are so large and there are so many the RBS doesn't have the nerve to pester them. Too, I added it years after the Bloody Parrots. Once your Parrots get settled down and it will take a while, chances are they will rule the tank. They will respond to aggression as a pack. This includes new additions to your tank. My RBS wasn't seen for 6 weeks after I put it in there. I thought he had been killed. Surprise!
Just keep your eye on things and don't let the aggression from your RTS get out of control if you can help it. I think they will all be fine in time as Shawnie mentioned.

Best of luck!
Ken
ps I'm moving your thread to the Cichlid/American Cichlid/Parrot Cichlid section of the form. I think it may help you to get more responses and help others concerning Bloody Parrots. Thanks! Ken
Here is the new link to your thread:
RTS and Blood Parrots...?