I've never been nude on stage. However, I did have to appear in boxers once. The story included a VERY strong vacuum cleaner which would "suck off" everyone's clothes if anyone happened to turn it on by mistake. In one scene I left the main room and came back in wearing a trench coat. My character was too dense to realise that he looked like a classic "flasher."
Saw a play once (Dare to go bare) where the guy was at the top of the stairs nude with only a tray covering him. He was supposed to walk down the stairs with the tray shielding him...... well his foot slipped and the tray went flying and be bounced on his butt down the stairs. There was about a 15 minute break where cast and audience laughed so much that they were not able to continue with the play.
I was nude in a play called BENT. I was comfortable being naked on stage, but was initially concerned when it was time for dress rehearsal because the lighting guy's young daughters were with him. And it wasn't so much me being nude that concerned me, but in the scene, a German soldier comes in, wrestles with me, and slits my throat. I was more concerned with the violence that they might see rather than them seeing my penis.
My first time on stage was in an innocent little comedy called Barely Proper. It was produced by my nudist club to promote nudism. It was a great experience, getting a laugh from the fully clothed audience. Later, I took some acting lessons and got involved in community theater. No other nude roles ever came along.
I'm a figure model for art groups and photographers, so being nude on stage isn't a problem. My 2 nude experiences on film were in "Fur" as an extra and as a body double in an indie film called "The Magenta Shamrock". I've always said if you can be nude in a room full of people, you can do anything.