It's unnatural in the sense that animal products are expensive, and require a lot of biomass input, and so it's weird to make them a dietary staple whereas most of the world lives on grains.

It's natural in the sense that it seems to be closer to the pre-agricultural diet of hunter gatherers which represents a much larger period of time in our evolutionary history than the relatively recent rise of agriculture. That's the idea underlying the Paleolithic Diet which I've had a lot of success with.