This is actually somewhat related to my line of work. The bottom line is, there is no simple answer because it all depends. If you take plastic shotgun shells, what are they actually made of? Some plastics (eg. polythene, PP) are relatively stable. Others like PVC or polyurethane deteriorate rapidly even under ideal circumstances. The decay cannot be prevented and is irreversible. While plastic objects degrade, they also tend to release a significant amount of gases. These are frequently corrosive (PVC is a good example) and will affect any other objects in the vicinity.

Even something as innocent as storing ammo in a wooden crate might be a bad idea. Wood, especially if not sealed, releases acetic acid. That means there will be a specific (slightly acidic) microclimate inside a tightly closed wooden crate. This may well corrode primers, bullets and brass cases and increase the rate of decay for many plastic shells. Most kinds of paper and cardboard are also acidic.

The damage is generally slight but cumulative. It really depends on other factors, mainly the room temperature and relative humidity (RH). As a rule of thumb, it's best not to keep plastic and metal objects stored inside the same tightly closed container. Anything plastic is better placed on open, ventilated racks, only lightly covered by something breathable to avoid dust accumulation. RH should definitely not exceed 60%. 50% or less would be a better (and usually still realistic) goal.

Folks living a dry climate may not need to bother with such safety precautions. In a very high humidity environment though you could store centerfire or rimfire ammo in a tightly closed metal box, perhaps with some silica gel inside. The gel will absorb excess moisture but you'll need to replace it periodically. It's reusable, though - drying can be done in an oven at 250-300°F for an hour.