This includes Ender Chests and Treasure Chests and Chest Mimics from The Aether (but not Trapped Chests)

good decision make that feature toggleable
ask to the mod author if he can make a fix, only have to add chest resources as a normal block.

otherwise, i will fix it in one month, but i had to attach aether resources on my mod, so is not the most ideal thing

Consider report this to the aether creators, they have to add chests as a normal block resource (adding block model and chest textures onto atlases)

i preffer avoid any problem related to include resources from other mods, use minecraft resources (for minecraft) is ok (i guess)

and if you ask, yes, i consider this as an option to a fix, but is not a hard fix on the other side

your picture show a Aether chest no rendering, no other kind of chests.
i didn't get any similar report... can you test few content mods with chest and emb++

This happens without Aether installed as well, so I don't see why that would be an Aether problem.

I also tried disabling block entity culling and that doesn't work either

I found the real cause. It happens only when I have one of the VanillaTweaks pack enabled, think It was either the "Proper Break Particles" or "Corrected Item Holding", probably the former
Just to be clear this only happens since Embeddium++ 1.2.0

well, that was expected, 1.2.0 introduces chests feature

+1 to being caused by VanillaTweaks.

Report issue to VanillaTweaks then