It can't be long before a militant nudism movement arises, inspired by other strident grievance groups to demand their rights. I can just see them shrieking angrily at "xtian haters" who want to deny them the right to go nude in public, just because they feel ashamed of sex and nudity and want to force their puritanical, xtian beliefs on everyone else. "Take your god-based bull and shove it--you don't have the right to tell me and mine how to live!!!"
I imagine these crusaders will ape the black civil rights movement, shamelessly trying to compare the restrictions that peeve them to Jim Crow while adding their own cute symbols and bumper-sticker slogans. "Bare is Fair!" Maybe they'll borrow a page from the homosexuals, and purposely go nude into small bakeries to order the cakes for their nude weddings. They could keep this up until they found a baker who was scandalized enough to refuse their business, and then sue him for discrimination.
I expect militant nudists will claim that just as with same-sex marriage, the state laws that frustrate them are arbitrary, because the government can't show how nudism hurts anyone. Even if public nudity is legal on certain beaches, etc., they will howl that their lifestyle deserves to be recognized everywhere, just like the clothed lifestyle is. And even if their own state had made public nudity legal everywhere, it wouldn't be enough--they'd insist that it was a constitutional right, so that every other state had to legalize it, too.