In the past I have used cellophane bags to package prints. As an attempt to reduce plastic waste, I have opted to instead wrap prints in recycled tissue paper bought from Eco Craft. More about them can be read on their website.
In the spirit of transparency, the tubes I use for posting prints in do have plastic ends, unfortunately. However, I am working on ways to ship prints safely and eliminate the use of plastics all together. Thankfully, the plastic caps and the card tubes can be recycled at least, or better yet the tubes can be used again (they make really bad didgeridoos though).