When I started selling seedlings, it was important to me to avoid plastic as much as possible. While avoiding plastic entirely is impossible for me, I have eliminated all single-use plastics from my very tiny nursery.
All seedlings that you purchase from GIY Chicago are in CowPots. CowPots are made from composted cow manure and are 100% biodegradable. Not only is there no waste, they have big benefits for plants - you plant the whole pot so there is no risk of transplant shock. Roots grow right through the pots, so they don't get root bound. And to top it all off, CowPots add nitrogen to the soil and break down in one growing season.
You can read more about CowPots on their website.