Double chests across chunk boundaries don't render from some angles/positions

The bug

Originally discovered by [Mojang] Panda in this video. To reproduce, place two chests across a chunk boundary (only some orientations may work), stand on top of one half, looking away from the two chests and move the camera up and down.

How to reproduce

Reproduction steps for standard superflat world:

1. /tp @p -272.73 16.88 257.53 92.55 62.45
2. /setblock -272 16 257 minecraft:chest[type=right]
3. /setblock -273 16 257 minecraft:chest[type=left]
4. Slowly look up and watch the double chest appear at the bottom of your screen