Shampoo and soap can dry out their skin, remove the oils/dusts from their skin and feathers, and in some rare cases, even result in plucking. Most parrots naturally produce oils that they spread over their feathers. This helps to protect the feathers from damage. Some birds produce dust as a form of keeping their feathers clean.
There are bird specific shampoos out there, but in general, I wouldn't recommend them! Water is best!
If a bird is experiencing dry/itchy skin then extra bathes, occasionally adding aloe vera to the bath water, or even using something like Soother Spray or Rain Spray temporarily from Harrison's Bird Products may be beneficial in the short run, but probably not good in the long run. Adding red palm oil/coconut oil/fish [liver?] oil (vitamin A and E) can also be beneficial to their skin.
But dry skin is most often linked to low humidity and a poor diet. Some supplements may cause more harm than good in the long run, so it's not good to supplement or add anything to their bathing water unless you know what you are doing.