Let me be a bit crude here to shed some light on the problem:
For a few years I kept my boat on a mooring a few hundred yards from the main marina. I tried adding the wind whirlygigs but the birds ignored them when it was calm. They would catch fish, clams, mussels, etc and bring them on top of my boat to eat. They would leave the fish and shellfish remains behind as well as their poop.
After a week or so in the sun this stuff would form a tough polymer like coating on the fiberglass. Fortunately I only had an aft bimini and they seemed to prefer the hard top to the sunbrella.
I tried everything including harsh solvents like acetone to get it off. The only thing that sort of worked was an electric disk sanding pad with a heavy coating of rubbing compound smeared on it. That would finally work through the coating without taking off too much gel coat.
I later found if I could stop it from happening by docking my boat at the marina, then after another few weeks in the sun it would begin to crack, crumble and turn to powder and come off much easier with just soap and water.
I realize that this won't help you with poop on the Sunbrella, but it's my story to tell, so I just told it.
David