How do I remove the glue from packing tape from the plastic surfaces in my refrigerator?

Acetone (nail polish remover)

Many solvents will injure plastic.

If this happened last year, you should have done this last year. Now the sticky stuff (not glue) has hardened, and will be much more difficult to remove.

I have always used a product called Bestine. It is "gum solvent". Or rubber cement solvent. It removes the "sticky" stuff that tape and price tags and other things leave behind. It's expensive, but doesn't generally harm things. You get it at an artist supplies store or a drafting supplies store. Get the small can. Don't leave the cap off. It evaporates quickly. I have a can from 10 years ago. I use it a few times a year. Like most solvents, it's flammable. Use it outside. Be careful.

This sounds weird I know but try using peanut butter. It's the only thing that worked on removing carpet tape residue for me.

Try using something oily, such as cooking oil or baby oil.

Also, WD-40 will often remove residue from tape and stickers.

I think there is a product called Goop Off. Ask at a big box store or hardware store.

Pam cooking spray and your finger.

get Goo-Gone