Tissue paper is known as a thin, semi-transparent layer for wrapping and void fill. While it is made out of recycled fibers, it is not recyclable itself — the fibers in tissue paper are too short to go through the recycling process again. A stronger alternative to tissue paper is kraft paper, but you lose out on the stock color options, light weight, and translucency.
While it won’t be turned away from recycling, tissue paper’s recycled fibers are at the end of their lifecycle and they are too short to be recycled into new paper.
Tissue only provides light padding, so you’ll need a lot of it to provide reliable cushion for breakable products.