We fully support Airbnb.org and what they are trying to do, but our current Airbnb.org guest has made it a miserable experience. How does this differ from an Airbnb.com booking? We didn't "donate" our place, but the booking was made through Airbnb.org. Did the Airbnb.org guest pay anything for the stay? Are they allowed to leave a review?
If you apply at Airbnb.org with a listing, you have to enter if it is offered for free stay or if it is offered for a specifc "limited price" (compared to the normal price). Usualy guests can not book directly on Airbnb.org, but only specific "partners" (organisations) can do so.
After booking it is managed the same as a "normal" Airbnb reservation.