An interesting question and one which I explored online a while ago when I had an idle moment. I'll limit myself here to the storage of snorkelling fins as I don't scuba dive. The following images of fin storage facilities and methods are from the websites of swimgear companies and snorkel tour operators:
1.
Aquam Canadian fin storage system
Here's the caption: "This wall-mounted unit allows you to hang approximately 30 pairs of fins on its painted stainless-steel rods. It may be mounted either in an equipment storage room or on the pool deck. In order to use this system, grommets must be installed on the fins which is a service we offer."
2. Snorkel Bob shelving system in Hawaii
Another shelving example:
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3. Aquagym French trolley system
4. Tour operator bin systems
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5. How not to store fins
Mould on fins in a swim cabinet at an American gym.
6. Advice and directives on fin storage
* Avoid unnecessary exposure to sunlight and air.
* Avoid contact with oils and greases, including sun creams and lotions.
* Avoid exposure to heat and contact with hot surfaces.
* Keep in a cool, dark, dry place in a box or bag. Do not distort during storage.
The Russian Standard on fins (GOST 22469-77) is the ony National Standard I know with rules on fin storage: "Rubber fins should be stored in packs in premises with ambient temperature from 0 to 25 ºC at least 1 metre from heat-radiating appliances and should not be exposed to sunlight, oil, petrol and other substances that deplete rubber."