Magic eraser? Theyre abrasive but if the fingerprints really don’t wipe off, that probably means the finish is etched or worn away. Vinegar is not something I would use in cabinets for that reason. The magic erasers might make temporary progress. I would also try diluted ammonia.

My cabinets are old and maybe there’s nothing that will get them clean. But the greasy fingerprints on the cabinet doors are driving me crazy. Is there anything that gets them off? I’ve tried all the regular cleaning products, dish soap, vinegar, etc.