Aboriginals rapidly caused the extinction of many species when they arrived, long, long ago. The species which they were able to exterminate were wiped out so long ago that we don't see it happening now. After a few thousand years things stabilised (that was many tens of thousands of years ago), and after that time they lived in an environment at steady state, not at all a case of them living here with an environment which wasn't being affected by them. White people came along, and did much the same thing, but it's still very early in the time of the white people, so we're still seeing the effects. If we jumped about 50,000 years into the future, we'd be able to say "Look! White people have been in perfect balance with the Australian ecosystems for tens of thousands of years! They're in perfect harmony with the place".
We are not living in the past, and the rules of today need to reflect today's situation, not the situation which existed many thousands of years ago. It's all fine and wonderful to say "They were here first, let them do what they like", but in some cases that just might lead to species, or at least populations, being exterminated. If it's sustainable, fine, let them eat whatever they like. If a species genuinely is endangered (and many of the officially endangered species are not, while some of the genuinely endangered species are not classified as such), then no one should be allowed to kill them for food. Australia isn't a place where it's easy to starve to death and we don't need to resort to killing endangered species. Culture is important, but maintaining cultural practices shouldn't be allowed to extend to wiping species out.