I grew up in a 1950's house and I live in one today. Many of them have built in cabinets that are stained red/brown on the inside. Any idea on what this stain is. I think it has some finish in it to smooth the wood somewhat. maybe shellac thinned way down with some tint. I do not really know why they stained them at all. maybe plywood was considered too cheap looking back in the day.
Bill D.