The machinery to make them, the fertilisers to grow them, the plastic to package them, the transport to deliver them. It ain’t just cooking oils that will be massively impacted. The entire food chain in the western world is reliant on petrochemicals. The only question is the lag between now and when those impacts start being felt and this translates into bumped prices and/or shortages.
EDIT: corrected an autocorrection.
Is there anything in that chain that actually requires petroleum and couldn't be replaced with alternative with similar properties and prices?