I'd considered this during the construction of the costume, and looked at the movie and press kit, and decided that they didn't wear anything. The cover of the issue of Rolling Stone magazine with Jeff Bridges, about the making of the movie, is quite obvious that Bridges isn't wearing a darned thing. I decided that accuracy called for my not wearing anything either.
I finally got the 20th Anniversary Edition of the DVD, complete with supplemental disc with a making of feature (and a LOT of other stuff) on it. Of course, after poking through the pictures and such, I ran the making of video.
It turns out I was wrong. Not only did the men wear dance belts, they were a running joke on the set. "How's your dance belt today?" "A little tight." It seems the dance belts were a little undersized, and made sitting painful - so the actors didn't sit very much while in costume. (For those of you not familiar with the concept, a dance belt is a cross between a jockstrap and a thong. The idea is that it provides support and, hopefully, a bit of concealment, while being comfortable even in extremes of motion and having no visible lines when worn under tights. Properly sized and worn, it's quite comfortable, but it can be irritating, to say the least, if it's not just right.)
Had I known that, I would have worn a dance belt - after getting one made in the proper size, that is - from the beginning. (I did wear one for the Jimmy Kimmel Live appearance.) I refuse to speculate on how that would have changed the course of history, or even how that would have changed the course of my personal history.