Not invasive as they are a native. Issue is the whole boom and bust cycle around breeding. More often boom. During boom years where food is plentiful they breed like well, rabbits. This applies pressure to their food sources which leads to starvation. It's worse is bust years particularly following a boom. Then they start invading paddocks and eating what feed there is reserved for livestock. Even though livestock are an introduced species. They are culled to avoid this and the inevitable starvation among their population that results.

That said there's usually somewhere around 45-50 million of them. So my point is. I don't understand animals rights activists sometimes. As much as they may hate it serves a purpose and if a byproduct can generate a revenue streams all the better.