Thanks for all the suggestions so far. Please keep them coming. I made a fabric liner from some raincoat vinyl backed nylon lined with denim. The fit was wrong. I didn't leave enough room for the corners where the uprights go through. It took almost an hour, so back to the drawing board. I did order 4 shelf liners from Amazon. If they are amazing, maybe I'll "bite the bullet" and buy more. I haven't been to the dollar store yet to look at placemats and foam board. The plastic canvas may work, too, and I will also try the doubled freezer paper suggestion. You all have such creative minds!!!

Not sure how big the baskets are but would a plastic notebook cover cut to size work? They are cheap and probably on clearance at the office supply stores.

They make those thin plastic cutting mats. You might be able to cut those to work. About $4.00 for 4 of them at Wally World. Just another suggestion.

Use cardboard
 

If your really short on money. Use cardboard. Cut it to fit the size you need. You can always go to the grocery store or walmart and get boxes free that you can cut up.

I have wire shelving units I bought at Bed Bath & Beyond. I used the plastic file folders, cut them to size of the shelf, punched holes in corners with hole punch, then zip tied to the wire shelf. You get two pieces per folder and the slickness of the plastic does not grab the fabric when removing. If you having the long shelving the plastic smooth shelving liner would also work, again zip tie the corners.

I use cardboard cut to fit. Sturdy, cheap.

This is what I 1st thought of to.

I went to the local picture frame shop and asked for boards that were cut-out from the center of the matts [they were free] then cut to measure for my shelves. Laid them down and they work great.

I would cover the cardboard with thinner fabric, and use the denim/vinyl for a picnic quilt : ) free fun.

you can cover cardboard with tin foil and their will be no acid to bother your fabric.
Learned about tin foil from one of my old quilting books! :)