Hmmm interesting question which I hadn't considered before.
I imagine fertilizers and manure would be okay for extended periods of time, probably best to thoroughly dry them first.
Soil holds so much bacteria etc life in it that I wonder how it would cope stored in say plastic bags or if that would eventually kill the bacteria. I wonder if keeping hot and cold compost beds and wormfarm in a working greenhouse at all times would be best. In a chemical type of attack you wouldn't want to introduce anything from outside the greenhouse so it would almost need to be functioning that way prior to the need arising. Water would be a problem as well unless you were getting from an underground spring because dams and tanks would be contaminated at least for a short time.

Organics will break down one way or another. Definitely faster if they are exposed to Oxygen. Bagged fertilizer should last indefinitely if not exposed to water or sunlight otherwise will deteriorate. The plastic bag it is stored in will likely be the first to go. The "dirt" should last thousands of years once the organics in it have broken down.

If you are storing your garden soil, dryer is better than wet for sure but it will still continue to decompose the organics and critters will continue to live until all their food is depleted. Even though it may have totally been used up, simply add water and you'd still have a growing medium. Just need to work to get it back.

My off the cuff reply would have been that the soil on my property is still doing OK after thousands of years just sitting there :p

What about freezing bagged soil? / can put alot of bags in a chest freezer

Sure why not. Like I said, keep the O2 out and it will last longer. Cool also helps. Even if it grows mould etc on top it will still be a clean medium to grow in later. If you store it protecting it from what you fear would contaminate it, then regardless of how it looks when you use it, it will still be good enough to get stuff growing in it.