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

Yes they have that ability. Whether it is wise or necessary is subject to debate. Before I would vote yea or nay I would like to know where you are stationed overseas. Livarno Italy is a whole different situation than Balad, Iraq. In Livarno, you would appear overdressed to the locals. I walked around a corner there and met a bunch of young women coming the other way. Some wore bras and shirts, most wore shirts and no bras and some had swimsuit bottoms and no tops. But in Balad, women were stoned to death for not wearing head covering so it really depends on where you are.
My advice is to remember you are REPRESENTING your country first and the service second in a foreign country and should bring disrespect on neither.
I was given the definition of an "UGLY AMERICAN" in Germany once. It goes like this - An ugly American is someone who can stand on a do it street corner in Paris, France and put his arm around his wife and say "Darling, if these blasted foreigners could speak English this would be a really great place."
The point that I got was that it was their country, not mine and I should respect what they want to do in their country and not just assume that we (Americans) do it right or even correctly.
Even in the Southern part of America where I came from we had a definition of a Yankee and a Damn Yankee which illlustrate this point.
--- Yankee - - Someone from up North - They are OK.
--- Damn Yankee - - Someone from up North, who moves down South and start telling us we ought to do it the way they did back home - They are irritating

I feel sorry for the male team leader who was put in the position of discussing female undergarments with female subordinate. In today's climate, a discussion that might not go well. This is a situation that the female platoon sergeant should have handled herself, if it needed to be handled at all.

If you can carry yourself professionally without wearing a bra then, wearing it may not be neccessary. However, bear in mind, it is unprofessional not to wear a bra in or out of uniform. Hence, a Platoon Sergeant has every right to correct that which he deems to be unprofessional wear in or out of uniform.

AR 670-1 has guidelines, not requirements, due to the fact that it is nearly impossible to regulate how your Soldiers dress when not on Duty. Depending on the situation, behavior or if someone brought it to my attention.
First, I would take it down the chain of command. The Soldier's Squad Leader should be the one to handle it. Truthfully, it would have to be pretty obscene for me to make it my business.
By regulation, an NCO should point out when a Soldier is dressed inappropriately. As Active Duty Soldiers, we are on duty 24-7, but, when a Soldier is on their time, I tend to keep out of their business unless it is bad.
Is it appropriate? Yes, is it overkill?

Yes...for the good order and discipline that the United States Armed Forces are known for; the US Military is not a club for high school tramps.

Article 134 “General Article”...”...service discrediting conduct...”

If that is not enough then discharge for FAILURE TO ADAPT TO MILITARY LIFESTYLE.

Have a nice ARTICLE 15 Day.

A new military to me - back in my day - when we were off duty we were not off duty - it’s a 24/7 job - appropriate professional attire was uniform of the day on or off duty - how the public views our folks in the military is utmost importance - there was no dressing down - boot camp should have laid the proper foundation for this issue - not after - I feel sure that JAG is reviewing newly drafted policy -

If this is now our concerns in the military, we are truly in trouble!

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YES. WHY? AR-670-1. There is a section in that regulation that governs how you wear civilian attire. As Long as you wear the UNIFORM, you have to abide by that reg.

I am so glad I am not serving anymore with the people in charge of their troops focusing on such petty crap as this. The military has turned into a bunch of whiney Karens, always wanting to be in other people's business just to make themselves feel better and get brownie points for stirring the pot.