Thanks for pointing that out. I hadn't been aware of it. The B4YOUFLY app shows the entire trail from Georgia to Maine as off limits. There are other similar Restricted Operations areas for the Blue Ridge Parkway and the C&O Canal Historical Park.
The Appalachian Trail is maintained by several groups/org but it is "Managed" through the USFS (National Park Service) and therefore is totally off limits to UAS unless the District Supervisor gives written permission for their use.
For the record, don't waste your time trying to get that permission because it's not going to happen. They have a blanket No Drone rule for every bit of the AT. The only way a drone can be flown on the A/T is for an active Search & Rescue or EMS mission.
To make it more difficult, several portions of the A/T go through Wilderness Areas which don't allow "motorized equipment" unless an Emergency Operation.