The "Receiving Remote Inventory" issue is a common one that can be seen in multiple cases throughout the game - usually while trying to access an inventory that is behind a structure or not within direct line of sight to the player, however in the case of Supply Drops there is an easy fix to make sure you can still get the items out of the inventory.
- Open the Supply Drop inventory
- Transfer one item from your inventory into the Supply Drop - don't put something important in, just a berry or a rock, something you wouldn't miss if something goes wrong while you're looking at the inventory.
- The "Take All" button should appear once you do this
- Tap the "Take All" button
- This will give you everything that was inside the Supply Drop