This might sound sacriligious, but I'd use a push pin; hang it front side out and take it down whenever I wanted to use it. Then both sides would be available. I have a colour wheel and like to hold my fabric against it, so hanging on a wall is not the most useful place.
Alternatively, you could laminate it, punch two holes in it, string the holes and hang it from the string. That way you could flip from side to side without taking it down.