Contests that don't allow alcohol in any form are relatively rare but they do exist, particularly down in the Souf. The prohibition may be due to the location of the venue, such as a city park, where local ordinances are in effect.
Then there are also contests like The Jack, which are held in dry counties. In Lynchburg, for example, the fine for having an open can or bottle of beer is $250 and the possibility of getting a tour of the Moore County Jail from an insider's point of view.
Even at contests where drinking is ostensibly not allowed, you'll see a lot of red cups for beer and liquor and the law will let it slide, as long as nobody gets out of hand.
Of course, there's always the chance of running across Barney with a bad case of badge poisoning who's on a mission to clean up the town but that could happen anywhere under any circumstance.
The answer to this is the same as with most other things in life: act like a responsible adult and you'll get along just fine.
HTH