Specifically regarding Black Boys, what was going on in that scene (other than making the Army look gay)? 
Was it supposed to represent a fitness hearing (a guy had painted toenails)? Why were they naked (it can’t be because they were already stripped from their physicals since they came in with underwear on)?
Yeah, I think it was supposed to represent a fitness hearing, but I wouldn’t worry about it making sense in any real world military way, any more than a guy who’s drafted in Oklahoma having to make his own way to Manhattan to be inducted. It’s all about setting up the musical numbers and the images.
I just love that song and that scene in the film.
In the original musical, I’m pretty sure it the song didn’t involve a draft board at all. The musical was rather…freeform, and the film did its best to impose some sort of linear plot.
When I was inducted into the Marines, for most of the physical we were in our underwear, but for part of it — nothing on. Yep, you’re checked down there too.
What I want to know is why does the “White Boys” part last longer than the “Black Boys” part?
I’m betting some white boys wrote that song.
For painted toenails?
Sure, but were you in front of a board of officers, none of them doctors, at the time?
Right. In the show (it’s even hard to say “original” musical, because it changed so much and so organically. It seems like very so often someone would glance back at the script and go, “Woah…was that what we were s’possed to do?” and send a new version off to the publisher for copyright reasons) it’s a “sharing” song sung by a bunch of girls just hanging around and Dionne (I think) starts singing about White Boys, and it just goes from there.
Lots (most) of the stage show is more musical revue that attempts to capture the feel and politics of The Tribe. The plot is wholey secondary to the vibe. Some of the rewrites made that even more so, and the current stage script is almost entirely devoid of plot. (There’s a little one in there about Claude and Berger trying to figure out what to do with Claude’s draft notice, but it’s pretty buried.)
The movie, on the other hand, tried to make a story out of it and managed to both suck and blow at the same time.