Currently you cannot open your inventory while underwater (unless you are inside SDV).
This is an issue for divers particularly.
In undersea operations, you should be able to open your inventory and vehicle inventories.
There are many scenarios where this is an important feature three of them include:

1. Taking a divers suit while underwater in order to survive (for special ops this is a useful ability especially - for instance doing a HALO jump into the sea)
2. Taking other divers ammo (Divers have limited UW ammo, so this is important)
3. Dropping items for teammates, looting dead bodies and getting ammo or items to complete a mission out of the SDV without having to surface/