When I copy the receipt from a assembler making rare copper cables to an Network Chest, the Network Chest is set up to accept normal copper cables instead of the rares.

Hi there, sorry for the late reply.
This is a known limitation — when copying recipes from assemblers to Network Chests, the game doesn’t provide any way to detect the quality of the items being produced. Unfortunately, Factorio doesn’t expose quality information through the recipe or entity data, so the chest can only request the base item (normal quality).
I’ve looked into this before when adding quality support, but there’s currently no workaround that i know of.If someone does know a Factorio API command or a way to get quality info from an entity, I’m all ears.