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

Unfortunately yes she can. We represent the Army and the United States on and off duty. Every word we speak, every action we take, and even how we dress is a representation of Army Values. Perception is a very powerful sense that people use. Some people see it as tacky and vulgar. Some people don't. It is the responsibility of our Army's leaders to remove ANYTHING that can be seen in a negative light within the Code of Conduct and AR-670-1. Leaders CAN and DO add to those regulations but they can't never take away. That is Army life young Soldier and it is something you have to get use too.

But really is this of importance to discuss or is it just to think about boobs? I say it’s not an issue and this is just to fill space with a story. Hmm maybe we should make sure we are wearing underwear too

While in recruit training, my drill instructors made it very clear what we could and couldn't wear. You will wear a bra, you will wear a belt if your pants have the loop holes for it, no halter tops, ect. Now I do not know if this is set for the Army.
I found this article, it is for Schofield Barracks, Hawaii but it seems to sum up what seems to be the Army Values in wearing civilian clothing.
https://www.google.com/amp/s/http://www.army.mil/article-amp/113110/usag_hi_to_enforce_new_guidelines_for_off_duty_attire

Hope it helps

I would say no except for special positions such as embassy duty or for particular details where appearance in an issue. Article 134 comes to mind, conduct unbecoming. An NCO with a chip on their shoulder can be a control freak and even if you have charges dismissed, it is still a pain in the butt.

That would be borderline sexual harassment in my opinion.

Maybe in uniform...not sure

Thye Navy has/had a simple way of dealing with these problems. Before leaving the ship, every enlisted below CPO must pass a brief inspection. If you don't pass, you don't get off the ship. In mu experience, there were many CPOs at the gangway so the inspection was pretty fast. There was almost never any reason for being denied a pass. Sailors figured it out pretty quickly and there were almost no 3-time denials. Very simple solution to a problem that seems pretty complex.

Yes, they can. In AR 670-1 every wear of uniform states "Undergarments" as part of the uniform. In DA Pam 670-1 ch 20-28(a) it states Undergarments for females is "Brassieres and underpants"

Unless you are bearing your boobs in an inappropriate place NO. Not just NO but F NO!! She is imposing her morals not the Governments morals. I would take her to task on the matter.

When a member of the US military is off duty their wearing apparel is their own business, providing they don't mix it with military uniforms.