I suggest using a deck cleaner and use it during or after a good or long rainfall. A deck cleaner will do a little better job than Simple Green but the soaking from the prolonged rain is the real help. Soaking, like soaking stains in laundry detergent, will help much more.
Protein stains are very hard to remove in general, but bird droppings are really tough because birds generally eat the things that Native American Indians used for paint colors in their art. These stains are in the “big leagues” so I suggest, soaking, applying the deck cleaner and brush scrubbing with a good hose rinse. This deck washing job is best done after or during a rain storm unless you have all the stuff that the professionals have with cleaners, power washers, stain treat etc.