How would I make the game update a texture on a block, or re-call the getBlockTexure() function? I need to update a tile entity's texture after it has read the direction it is facing from NBT.

or use meta, or use a tile entity special renderer, because both these method are way easier to do

Thank you meta worked!

well sort of, how do I make it be on a certain side in my inventory?

if youre using meta on placement well its never gonna be in a certain direction in your inv because in your inv it doesnt have meta

same for tile entity, in your inv they dont have a tile entity

yeah but is there a way to set the texture but have the meta override it?

 

no, you could try your luck with a IItemRenderer and using the nbt of the itemstack as holder for the "meta"

How does a furnace do it then?

Well look at BlockFurnace. Mojang use two block ids.

 

You could use ISimpleBlockRenderingHandler to do render passes accordingly to a tile entity.