Government shutdowns are very confusing events, and it's not always exactly clear what happens with things like National Parks. Different things have happened during different government shutdowns over the years. Not all shutdowns are the same. Administrations have important decisions to make about actually locking the gates.
Native American tribal members with historic hunting rights here in Montana and Wyoming were allowed to hunt bison outside of Yellowstone National Park. Big city environmentalists freaked out because they thought too many bison were killed in such a relatively small area.