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

Wearing undergarments is a personal choice as far as civilian clothes. I am sure there are a number of male commentators on this post who have gone "commando" while in civilian attire. I doubt if any of them have been counseled to wear undergarments, even if the chino trousers they are wearing are a size or two smart.
With this being said, there is the idea of representing yourself appropriately while serving overseas. I would certainly have asked the PSG what was the basis for her decision to direct the wearing of a bra while in civilian clothes. Are other female soldiers in the unit getting the same directive? Are other females int he same company getting the same directive?
No matter what, we have to realize we are only getting one side of the situation. We don't know the rationale from the PSG. We don't know the guidance from the local commander. What would be appropriate attire for Taegu, Korea may not be appropriate attire for Doha. There may be other issues in play here.

This question says "Posted 1 y ago", so I wonder why it to so long to appear here. There are a lot of good comments already. I will briefly mention one aspect: "...on rotation over seas." What Country?
Army (all branches) are invited or permitted into foreign countries by what is termed "SOFA" (Status Of Forces Agreement). Among many other things, the SOFA specifies who has legal jurisdiction and may spell out certain regulations and behavior of Service Members. The Service is responsible for Military member's behavior almost entirely. I spent two tours overseas in the Navy in Japan. Unlike being off-duty in the USA, where you can exercise your constitutional freedoms, being off-duty in a foreign country is much like being on-duty. The Senior Officer in the host country, in my case, Japan, is CNFJ, spends a lot of time, on community relations and dealing with incidents between US Service Members and the Japanese population. To step back from specific issues, the regulations for Service Members station in Germany or Italy might be entirely different than for those station in Saudi Arabia.

Yes you do need to wear on. It is in respect for the nation that you represent and the institution that you are affielated with.

I don’t understand how this is even a question.
Why would you want to wear something like this in the first place?
Just look professional around the people you work with
When you are alone away from coworker wear whatever you please.

I will say that you did open up a subject that could be difficult and possibly offensive to a lot of women.. Dress well, conservatively, and appropriately. Enough said... Gunns

I for one simply told my gals that you are fighting gravity all your life. Personal comfort now might bring further problems later in life. Sports bras will give you comfort and support in daily life as well as in sports/mil training events. I used information gained from the women in my life. they pretty much told me that if you want your breasts down around your waist later in life, then don't take care of yourself. Well, that becomes a matter of choice for a woman. Still, if the regulations say wear one, you need to wear one. Some women don't have large breasts, so the problem is minimal. Others have major problems in support and containment. I have lots of sisters and aunts who have problems and they say that appearance in your clothes has a lot to do with bra or no bra. You take it from there.. Also, do you want to be on the skyline with your leadership most of the time? You have a choice on what you want to do... One from the Gunny's desk.

There is no official regulations on undergarments outside of religious use. This is a personal matter honestly. Do as you please and if she continues to talk to you about it I would look into the post regulations.

Technically there is no regulation for it so no you do not. Her reasoning for it is simply personnel

Why is it that women in all aspects of life try to fight any sort of dress code? It seems that women of all ages and throughout every single stage in life try to fight their schools, their employers, and even the military about letting them dress however they want to instead of how they know full well how they are supposed to dress according to any of the rules and regulations. You're a soldier in the U.S. Army and whether you like it or not that is part of being one and all part of everything you agreed to when you signed and took the oath. This is really such a simple thing to even adhere to and why someone would even try to make this a bigger issue is beyond me, seems so simple to just shut up and just do what you're already supposed to be doing in the first place.

All I can you to do, besides AR670-1 check your post regs. Each Post Commander has his own policies. You can always add to but never take away from Regs. One more thing, pull your PSG aside and talk to her.