Are we just talking about a poncho that does not make noise? Presumably able to provide weather protection?

If so, maybe it's time to look a little to the past. The old stuff was used for centuries, because it works.
Personally, I use wool. High quality, heavy wool will be waterproof in light-medium rain. For heavy rain, I use waxed canvas. The 2 combined also make a great bedroll.

 

Sitka Gear makes some quieter goretex options but they are pricey.

 

I use a poncho for canoeing and can see the advantage they would bring to bow hunting from a stand. Good luck finding a quiet one though. Quiet and poncho would be a very tiny niche market. Maybe you can find one on Pinterest?

 

Try looking at a military surplus shop