Alcohol is allowed, though not in the campgrounds, youth camps, or in public buildings i.e. Nature Center, Reservation Center, etc.. The park does provide non-alcoholic refreshments at the beach and in the camp store.
From the official website. (http://www.in.gov/dnr/par...)"Alcohol: is strictly forbidden at Indiana Dunes State Park and in all youth camps. At other properties, both daily visitors and campers are asked to be responsible when drinking alcohol. Possession of alcohol by persons under the age of 21 is against the law in Indiana; and this will be enforced."