Bryant RedHawk wrote: they all are based on the "Elmer's carpenter's glue recipe"
Classic white or yellow wood-workers glue (Elmer's) used to be made from cow hooves and other connective tissues from horses and cows. They even had a cow integrated into their logo; Elmer the bull, mate of Bordon's Elsie the cow. Today, wood glue is made of synthetic ingredients, but perhaps you could find someone who still manufactures wood glue using the classic cow-hoof formula (hydrolyzed keratin). That would be benign for your soil. Jello is pretty much made of the same stuff—if you would not be concerned with dumping a dish full of lime jello into your
compost pile, you wouldn't need to be concerned about using classic animal-based glues.
But does anyone
sell that stuff anymore? A quick search of the interwebs turned up nothing for me. And I'm not too sure how long it would hold up in a consistently wet environment like a
raised bed.
I'd use mechanical means to hold those boards together: nails or metal screws. If they rust, that's not a problem—it just adds to the iron in your soil and your plants will appreciate that. Or use stainless screws that will not rust if you want them to last forever. Or wood pegs? Is there a way to connect those boards using cedar pegs? Its not like they have to bear a lot of weight or anything --- they just have to sit there on the ground and keep the soil in place.
"The rule of no realm is mine. But all worthy things that are in peril as the world now stands, these are my care. And for my part, I shall not wholly fail in my task if anything that passes through this night can still grow fairer or bear fruit and flower again in days to come. For I too am a steward. Did you not know?" Gandolf