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

Short answer: yes!
Long answer: don't be fucking stupid. You're body belongs to the gov't and the civilians who pay taxes. You don't belong to yourself, while in uniform.

Okay, it does not state it directly, but it does state this in AR 670-1 dated 26 January 2021:

3–6. Uniform appearance and fit
a. Appearance.
(1) All personnel will maintain a high standard of professional dress and appearance. Uniforms will fit properly; the proper fitting of uniforms is provided in DA Pam 670 – 1. Personnel must keep uniforms clean, serviceable, and roll- pressed, as necessary. Soldiers must project a military image that leaves no doubt that they live by a common military standard and uphold military order and discipline.

Chapter 4
Combat Uniform
4–1. Authorization for wear
The combat uniform is authorized for year-round duty wear by all Soldiers, when prescribed by the commander. Some combat uniforms are classified as utility uniforms, while others are designed for a specific function. See DA Pam 670 – 1 for uniforms currently classified as combat uniforms.
4–2. Composition
The combat uniform consists of the following:
a. Coat.
b. Trousers.
c. Undershirt.
d. Undergarments.
e. Belt.
f. Socks.
g. Boots.
h. Headgear.

Bottom line: Check the Regs and SOPs for your unit and if in doubt you have a legal office which can confirm what's authorized and not authorized...hope this helps.

First Sergeant Johnson is absolutely correct about the uniform issue; and, you did get an answer her that you can actually use in this situation by reading his response. And, it's been a long time since this was originally posted. Personally, I'd think twice before allowing it, but only as long as it took to make a phone call to the CSM and ask if he or she had heard about it. I frankly think we all have better things to do. In today's Army -- and I've been retired for 34 years now, but in my Army as well -- soldiers can demand an answer to things that look like exaggerated interference. And when you get into the ambiguous realms of things like "will present a professional image all leaders need to seek clarification. Hence "local regulations."

This would be my own personal NON-answer (and it may appear slightly sexist) it would depend on the build of the female in question, and what she was wearing. If she is flat chested (to put it bluntly less than B cup), and NOT wearing something revealing I would not say something about it! Now, stating that my active duty service was prior to females being allowed aboard combatant vessels, if that female had enough to cause a distraction (or her clothing fit was) I would probably 'suggest' that she find some better supporting garments.... (I have seen females from tenders (back then the only ships that let females aboard) with a bikini top under a wife-beater (tank-top t-shirt) get asked to put on something less revealing for a shirt.

Go have a conversation with your PSG and ask that another be present with you. (someone that has not been in trouble) Listen carefully to what She has to say, then decide if this is worth taking to the IG or not? If not let it drop and do as you are told. You could create yourself a lot of future grief over this or maybe end your career. This is not cheerleading this is the Army, many of your personal freedoms are gone. You know this already unless you came in as an E-4. My advice is to follow directions. She did not single you out just to have someone to harass.

AR 670-1 only says this about civilian clothing.
3–9.Civilian clothing
a.Civilian clothing is authorized for wear when off duty, unless the wear is prohibited by the senior commander. Commanders down to unit level may restrict the wear of civilian clothes by those Soldiers who have had their pass privileges revoked. Within the confines of a military base or a DoD installation, civilian clothing will be worn subject to local regulations.
b.When on duty in civilian clothes or off duty and outside of their personal dwelling, Army personnel will present a professional image that does not detract from the profession, unless specifically exempted by the commander for specific mission requirements.c.Soldiers are associated and identified with the Army in and out of uniform, and when on or off duty. Therefore, when civilian clothing is worn, Soldiers will ensure that their dress and personal appearance are commensurate with the high standards traditionally associated with Army service. Commanders are charged with determining and publishing the local civilian clothing policy. When on a military installation, civilian headgear will be removed indoors in accordance with established norms.

This could just be his opinion that not wearing one is not "commensurate wit the high standards traditionally associated with Army service," or that it doesnt present a professional image and detracts from the profession.
You could ask for the local civilian clothing policy that according to regulation should have been published.

DAM 670-1 does state a bra will be worn while in uniform.
20–32.Undergarmentsa.
Brassieres and underpants (female).(1)Type.Brassieres and underpants are a one-time cash allowance purchase as part of the initial clothing bag allowance.
(2)Description.Brassieres and underpants may be of a commercial design in white, black, or other neutral colors that are not readily apparent when worn under the uniform. The category of brassieres also includes sports bras.
(3)How worn.Female Soldiers will wear brassieres and underpants with all uniforms.
b.Camisole (female).(1)Type.The camisole is an optional purchase item.
(2)Description.The camisole is of a commercial design in white, black, or other neutral colors not readily apparent under the uniform.(3)How worn.(a)Female Soldiers are authorized to wear the camisole with all uniforms. The camisole is not a substitute for the tan 499 undershirt when the tan 499 undershirt is normally part of the uniform,such as the ACU, flight uniform, cold weather uniform, and so forth.(b)The camisole is not a substitute for brassieres. Female Soldiers will ensure that uniforms fit properly when wearing the camisole.

No. Period!

New job=No bra required. Strip clubs, (Gentlemen Club) or even Hooters. Members, don't know the local policies for your duty station. Your chain of command does.

Simple answer is yes in accordance with the UCMJ. Anything that brings dishonor to the Uniformed Branch is punishable under the UCMJ. All of the service branch’s have regs that reflect that for their individual branch. Also what you say off duty, if it reflects badly, may find you in trouble with your commander too. Even retirees if they receive benefit payment can be prosecuted for their actions and /or speech.

I am not smart and this might not amount to a hill of beans, but the last thing I would care about is whether you wear a bra or not amongst civilians. What next? You can't wear pants that show you have a butt crack?