I'm no scientist, but the effort that goes into cleaning a peanut butter jar must outweigh the benefit of recycling it.

I usually fill them with hot water and Dawn and let them sit for a day or two. The leftover peanut butter rinses out pretty well after that. Fill with hot water again to loosen the glue holding the label on, peel it off and then use a mix of veggie oil/baking soda to get residual glue off.

It then goes to the garage where it is used to store hardware.