Have the mobGriefing gamerule not affect allays at all.

Since allays spawn without an item, they will never start "griefing" by picking up items on their own. They will only do so, after the player has explicitly given them an item and asked them to do so.

Splitting this behavior into a separate gamerule would be an alternative to keep this current behavior (although, personally, I don't think there are a lot of use cases for this).

Finally, yes there are already plenty of other "split up the mobGriefing gamerule" suggestions, but I think this one is slightly different. All the other behaviors can happen without any player interaction. Of course, it might still make sense to split them up, but all of them I would indeed consider as "griefing" and they do fit the current gamerule (which is just a bit too generalized atm).