Thanks, everyone! I assume that the pieces are from two different original rabbeted pieces of wood which weren't matched after cutting.
When I put the plate on the crate and apply some pressure, I can push it until it hits the lower rabbets. Over time and with the weight of all the components it will probably bend. Even if not, I agree that the plate should be held evenly and solidly on all four sides. That's the whole purpose of having four rabbets, right? I guess I need to find some thin strips of wood (craft sticks, popsicle sticks, maybe) that I can cut and glue on before staining and finishing but would not want to work with plastic or tape. Maybe I do when desperation kicks in.
When I took the photo, the crate was lit unevenly, which explains the darker and more saturated color. The wood is same throughout.