I wouldn't find this appropriate in a workplace, would you? Would this truly be a double-standard to say that nipple show would be so discriminatory?
For the record, my employer has always had an undergarment policy. It was stated that "appropriate undergarments must be worn." Where I work scrubs are fairly standard(and they are not made of very thick fabric) and I have always taken it to mean that you shouldn't be wearing hot pink underwear beneath your white pants. Though the policy certainly did allow management to step in and say something if something was found to be inappropriate. I actually have gone braless at work (on a rare occasion) I had an instance where I had this horribly uncomfortable rash that would have made it pure hell to have a bra on. I made certain that I had on other clothing beneath my clothing that prevented nipple show and certainly no one would have thought I was dressed inappropriately.
Of course the approach that a manager makes to you would certainly make all of the difference in the world. If done incorrectly I could imagine a sexual harassment suit occurring, I would think a great deal of professionalism would be called for.