River Paddling Protection Act - Opens the rivers and streams of Yellowstone National Park and Grand Teton National Park in Wyoming to hand-propelled vessels. Declares specified regulations to have no force or effect with regard to the closing of rivers and streams of such Parks to such vessels.

Requires the Fish and Wildlife Service to coordinate any recreational use of hand-propelled vessels on the Gros Ventre River within the National Elk Refuge in Wyoming with Grand Teton National Park to ensure that use is consistent with the requirements of the National Wildlife Refuge System Administration Act of 1966.