Changing Room Help! Watch
Not like anyone's going to bum you to death.
It's ludicrous to keep your underwear on. Generally if you want to avoid comments from people (in most situations, not just this one) you have to act like everyone else. Since life is certainly easier without hang-ups, just force yourself to go naked and you'll probably find you've been worrying over nothing. Once you've done it once, I doubt it will be an issue for you again.
Other words. Just conform and never ever, and I mean never, stick out from the crowd.
What I meant to say is that, in this instance, the majority are showing him the way and if his goal is to avoid embarrassment then, counter-intuitively, the OP needs to strip off. Since he'll also get more clean that way and lose what I feel is excessive inhibition then it's nothing but upside.
Obviously there are situations where it's important to follow your own instincts. I just don't think this is one of those situations.