First, I am not flying in a reserve. If you notice I am using a zoom lens far from the bird. Do the bird looks distressed for you? Do you realize people walking with dogs in a reserve distress more animals that taking pictures from far? same as photographers with zoom lens. No difference.
This is all about common sense. FWC allow hunters to kill and hunt migratory birds. Do you know how loud is the gunshot from a shotgun? That will distress even people in a 1/4 mile radius.
Yes, a reserve or national park is different and we need to follow the rules. This is why is important check the area to know if is legal or not. I always use
SkyVector: Flight Planning / Aeronautical Charts before flaying in a new place.