You do realize that there’s no such thing as an ecosystem made up entirely of animals, right?
So if there are no plants to eat on this island, it’s likely that there are no non-human animals, either.
So what if you were stranded with other humans? This is, of course, a much more likely scenario, as most of us don’t travel over oceans without the company of others. So you are on a desert island with nothing to eat except your human companions. Do you wait until one of them dies and then consume his remains? Or do you become so hungry that you decide to use your remaining strength to kill the one who is weakest and likely to die first? And what would be the moral implications of either of these actions when you are not in the survival situation? The answer, of course, is nothing. Whether you participate in cannibalism or murder in a survival situation has absolutely nothing to do with whether or not it is moral to participate in those actions when you are not in a survival situation.
What this question fails to acknowledge is that killing for necessity is not morally equivalent to killing for pleasure or convenience.
A much more relevant question is the following:
What if you have a choice between getting all the nutrients you need by consuming fruits, vegetables, beans, and grains, all of which are readily available at any grocery store, or you could consume a diet that requires cruelty, exploitation, and slaughter and which contributes significantly to climate change, deforestation, water scarcity, water pollution, ocean dead zones, habitat loss, species extinction, and world hunger?
Given these alternatives, which would you choose? That’s the real question that the overwhelming majority of us face.