Because mineral oil isn't a "drying" oil (it doesn't polymerize in air), it's an unlikely choice for finishing furniture because it stays greasy and will rub off on things.

More likely is a drying oil, like linseed, or a synthetic finish, like polyurethane or epoxy.

I was thinking of bamboo kitchen items. I know he said toothbrush so maybe I typed too quickly

Some use fish glue (though still using petroleum and causing a majority of microplastic ocean pollution via the nets).