Can a platoon sgt tell a female soldier that she is required to wear a bra when in civilians?

On duty ? Absolutely. Off duty if it detracts from a professional apperance. It is subjective and depends on the person's body. In theory you could challenge it by going up the chain but my guess is it's not worth it. As a personal anecdote during a civillan clothes PT day an extremely embarrassed female platoon sergeant told me I was required to wear briefs and not boxers while engaged in running/jumping on base. So this is not solely a female issue.

Did the PSG elaborate on her rationale for this?

I think the best course of action here is to ask your team leader to schedule a meeting for you with the PSG and ask the PSG for clarification on what you did or did not do to necessitate receiving the directive. "Generally" there is a good reason for something like this that just didn't get filtered down to you. Either way you'll get far better results than all of the answers on RP.

The simple answer is yes, of course she can. The reason she issued the order is irrelevant. There could be a multitude of reasons why. Unless you have a valid reason for not complying with a lawful order you can and likely will be held accountable.
Don't let something so trivial trip you up. If you are serious about your career you will need to learn that you will sometimes have to sacrifice comfort and individualism for the greater good.

Put the bra on, child, and quit whining! Look at all these nice men trying to be PC & not step on your feelings...it's irrelevant! If you can't follow this simple request, you don't belong in uniform. Your personal beliefs are irrelevant especially when you represent women in the military and all we fought for to achieve to be allowed to even wear a uniform. Out of the country is even more imperative. Do you not realize this is basic traing bs? You were told to wear the bra, wear it...suck it up, buttercup!

Current Rotation Overseas doesn't tell us where which, can make a big difference. Arabic countries are going to see things differently than the local dance club in the US or Germany. That said, if the PSG wants to say something, they need to say it, not pawn it off on a Team Leader. That's like me telling my kids to tell another kid how to dress at school. The PSG can include the Team Leader in the discussion/counseling, but it's not his job too do the PSG's job. Good Order and Appearance is so subjective it's probably actually worth asking for a "proper counseling" on a 4856 so you are not fighting "a audita pro compertis" (hear say) battle and you have it in your personnel file. Remember you do not have to agree with the counseling, but make sure your reply statement accurately reflects the facts of the counseling, not your opinions. Elevate it if you want the fight, but don't put emotion into it. I would maybe go so far as to include pictures of the "offending" clothing (not unlike the Tattoo Picture Policy) as examples to show clear evidence of your civilian attire. I'm betting it won't go past Co level, the LT or XO could put a quick stop to it at a Platoon level. You may win the fight, but it could put you in the line of fire too, so choose your battles. A simple solution would be to comply when in the Co/Post area, and once you are out on the town, take it off and go about your business.

I read a comment where a Male said they wouldn't address a Female about this. That is also a wrong answer. Get over yourselves when talking to the opposite sex. If you're willing to type it out on RP, then Man Up and be a leader to your Soldiers.

This seems like a really strange request tbh. However, one thing that caught my attention is that you're on a rotation overseas. First, this means that "off duty time" may be a little more regulated than when you're CONUS (I'm not sure of your unit, security situation, mission or anything so it's just a guess). Second, there could be a cultural reason your PSG is giving you this directive. For example, if you're in a place like Kuwait and around locals, I can see how a tight fitting shirt and/or going braless may cause friction with the host nation - something the Army as a whole is sensitive to. Is that fair to US servicewomen overseas? Probably not but unfortunately that's the world most people live in.

Again, I don't know the specifics but it's something to consider.

DA Pam 18-30 Undergarments...check it out. You will wear that shit in uniform. Now that we have that out of the way.

So it must clearly be making someone uncomfortable that you aren’t wearing a bra in civilian clothes. Put one one, drink some water and march on. Pretty easy.

SFC JOHNSTON is completely on point. From a female perspective, we must maintain a professional appearance at all times, in or out if uniform. Unfortunately, that is subjective and vas

When I was in the Corps, we (male and female) were told basically what we could wear Off Base and that at All times we were 24/7 in the Corps and should Always dress Appropriately. We were never given any Regs or rules on what was Appropriate, but we knew and most all the time adhered to being a 24/7 Marine even in civilian attire. Of course I cannot speak for everyone.
I do know that when on base in civies we always dressed appropriately.
Much later after the Corps I worked for the Army and I often saw Soldiers dressed like crap, sloppy, when in civies and sometimes even in Uniform.
So if there is no reg I would think she can dress as she pleases. But I would not want to PO my Superior Non Coms and would say fine and then wait until I was out of sight.