If you are on a team, invisible, certain entities do not render through the invisible player. Not having much time at the moment, I was able to compile a few of these entities that do not render through the player. These include:
Armor Stands
Chests
Chests, Furnaces, and Command Blocks in minecarts
Cows
Creepers
Dolphins
Donkeys
Ender Chests
Items (on ground and in hand)
Item Frames
Trapped Chests
Picture below is an example
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This is one of the differences between Fancy and Fabulous, see MC-187783 for developer confirmation.
What is your "Graphics" set to?