Oil paintings are uniquely delicate because the paint surface itself can smudge, crack, or stick to any material that presses against it, and unlike framed prints they usually have no glass to protect them. Temperature swings also crack aged paint. The rules are to never let anything touch the painted face and to keep the piece climate-stable.
Pro tip: Glassine is the archival standard because it will not stick to or react with oil paint.
Watch out: Never let plastic, bubble wrap, or paper adhesive touch the painted surface. It can stick to and lift the paint.