A few bugs have been reported on parrots making hostile sounds when no hostile mob is around. This is the case even in peaceful mode. The bug MC-115509 describes this well but has been marked as "Works as intended". Well if this is how it is supposed to work then peaceful mode is not that peaceful after all.

I have a 6 years old son who is afraid of the sounds in normal mode so we play in peaceful mode. I have even turned the sound of the weather off so the thunders don't scare him. But now we have finally found a jungle and some parrots. The parrots are making scary sounds and there seems to be no way to avoid this.

I think you should reconsider if this "works as intended" as this does scare young kids playing in peaceful mode.