The correct answer to this open question is the following.
Did the Australian Government have the right in 1987 to propose a UNESCO designation of Ayers Rock/Uluṟu as a natural and geological site?
Yes, it had. It's part of the Australian territory. Indeed, in 1958, had declared as an Aborigen Reserve. It is understandable that the proposal to the UNESCO designation had created some discordance and controversy in that Uluru is a sacred place inhabited by ancestral native people, but the government of Australia has always respected this tribe and its traditions.
Aboriginal people consider the place as sacred. Tourists can visit but they are not allowed to climb the mountain because the Ayers Rock monolith represents a spiritual place according to Uluru's creation story. So the Tourism Department of Australia has shown respect for the aborigen people traditions, culture, and customs, and has established a permanent dialogue to facilitate visits asking tourists to show the kind of respect needed to never mess with the people, traditions, and to produce any affectations to the rock.
