MILLN REEF, Australia — Murrumu of Walubara and his son, Thoyo of Walubara, paddled in the clear waters of the Great Barrier Reef, among corals of electric purple and burnt orange, trumpetfish, sea cucumbers and giant clams.

They were 35 miles off the coast of Australia — or, as Mr. Walubara says, what most people refer to as Australia.

To him and his followers, the Great Barrier Reef is a part of the Yidinji Territory, a self-declared nation spanning more than 6,000 square miles in the northeastern part of the continent, which Mr. Walubara formed in 2014, but to which he says sovereignty was never ceded.

Five years ago, after realizing that as an Indigenous man he was not recognized by Australia’s Constitution, Mr. Walubara quit his job as a political reporter and renounced his Australian citizenship and former name, Jeremy Geia. He returned his passport, public health care documents and driver’s license to their respective government departments, he says, and destroyed his Australian bank cards.