I used to buy firewood at National Forest camping sites in the US; there was a box where you dropped the money and then you grabbed a wood bundle.
Granted, this was almost 40 years ago, but this type of thing can work, even in less civilized places like the US.
They leave out more wood than a camper would even think to take because they only need one bundle every day or two. The sort of person who would need to steal a whole season's worth of wood is less likely to have the means to transport it all, and if they're so desperate that they'd go to the trouble then the Christian thing to do would be to let them have it.
Gillette razors on the other hand, are expensive to stock for their size, and easy to steal because of their size.
I’d wager that outdoorsy people who are out camping in the woods are like a “mini-Japan”. The community has their own set of rules and behaviours that would make an honour system possible. Especially 40 years ago when it would have been more of a monoculture.