I see where you’re going. The old Wiki route or whatever.
Sorry. Hunting as a “way of life” precedes agricultural by many tens of thousands of years. They would have been familiar with animal fats/lards way, way before they learned how to press/squeeze an olive. Ever eat a raw olive? Bleh!!!!
They weren’t “gatherers/hunters”.
They were “hunters/gatherers”.
Anyways not worth arguing about...
Soap is recent. The romans didn’t have soap. So your soap theory doesn’t hold up.