In a healthy home I personally would not consider shelf and drawer liners made of PVC including fabric backed with PVC, rubber, or cork (which is pressed together with a polyurethane adhesive).
I consider EVA, polyethylene (PE/PET), polypropylene to be safe healthy plastics, especially for this application.
Other non-toxic, eco-friendly options include paper, fabric and wood veneer.
The following options are made for shelves, drawers (kitchen and other rooms), dressers and wire carts,
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1. EVA Plastic Liners
I like non-PVC plastic liners with no adhesive on the back.
I like this clear EVA one from Amazon.
You can also get a solid color for a heavy-duty EVA Drawer Liner (also non adhesive).
IKEA also makes EVA liners.
2. Silicone Drawer Liners
Silicone is very grippy – good for drawers or anywhere where you want things to grip to it.
Silicone liners are non-toxic, I find I need to air it out for a few hours when it’s brand new.
3. Polyethylene (PE/PET) Liners
Polyethylene is easier to slide items across and so it’s better for kitchen shelves.
I have seen them at the Container Store and these cute polka-dot ones from Amazon.
4. Polypropylene Liners for Wire Shelves
These are a thicker and sturdier plastic used to add a stable layer to wire shelves.
Polypropylene (PP) is one of the safest plastics.
Gorilla Grip specifically states that their liners are PP.
5. Paper, Cloth & Wallpaper
When I was a child we used paper to line our kitchen cabinet shelves and drawers so I’m partial to this non-plastic look.
Some of the old-school ones are actual paper, but they are harder to find. The paper ones I usually see are now backed with PVC.
You can use an actual wallpaper. And a non-toxic wallpaper glue if you prefer that look.
Spoonflower (pictured) makes a PVC-free peel and stick wallpaper that is available on Amazon. Their wallpapers have cute designs and work as shelf liners on many surfaces.
You can use fabric to line shelves but you normally find this backed with PVC to make it stay in place. I would use a non-woven or cloth wallpaper (that is PVC-free).
For bedroom shelves or drawers you can use a wood veneer liner.
This cedar liner is only wood, though the reviews describe it as finicky.