I was in Naked Boys Singing and for me, being naked was simply a different form of costume. Unless you are involved in a scene with sexually suggestive physical contact, I really doubt there would be any danger of popping a boner. Even then, it would probably have to involve someone you find attractive, and awareness of the audience would still probably kill it (unless you're into that). The biggest problem was when you feel the urge to pee. As most guys know, when the little soldier gets some fresh air, he wants to go and he wants to go NOW, whether it is necessary or not. That is horribly distracting when you are performing an entire show in the nude because it would happen totally at random.
As for Hair, I saw a brilliant performance by a small theatre in Dallas in 1988 which had two moments of nudity. The first opened the Hare Krishna song, when a girl in a gauzy peasant dress starling twirling around and around. The dress billowed out a bit and the lighting illuminated her naked body underneath the garment. It was stunning. The second involved a man who was dragged out onto the stage in a fully zipped body bag. A couple sang What a Piece of Work is Man and he emerge from the bag completely naked as if it was his birth. He then moved in slow-motion throughout the song and struck a pose reminiscent of Da Vinci's Anatomy of a Man. At the end of the song, he slowly died on stage, was zipped back into the bag, and dragged off the stage. It was poignant and beautiful.
I attended the 25th Anniversary national tour of Hair. I don't know if there was any nudity because I left right after "Donna". It was one of the most embarassing productions I've ever seen.
"What can you expect from a bunch of seitan worshippers?" - Reginald Tresilian