It depends on the laws in the states and local Jurisdictions however on a beach it's unlikely that anything will happen if you wear just a diaper because most people on beaches are wearing Speedos or one or two piece bathing suits.
I wore an ABU Little Pawz diaper to the beach last summer and played in the sand wearing just the diaper and a T Shirt and I did get a few giggles from a few girls and a few guys laughed at me but it didn't bother me as I was having fun and minding my own business.
Cops walked right past me and never said anything either.
It took me awhile to get the guts up to wear just the diaper in public on a beach but I'm glad I did because it was very fun and I plan to wear just a diaper on a public beach again this coming summer.