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

I do understand you position as I was once told that I didn't have on any socks while in civilian clothes and off duty. I simply asked for the reg. be presented to me to suggest that I had to have them on. Good fight, and it sounds like somebody is just a tab bit envious.

Yes he can, you are in a TOTALLY CONTROLLED COMMUNIST JOB...ONE PERSON CAN BREAK YOU OFF/DOWN and YOU HAVE NO CONTROL....Pray you have Americans and not the Dumb as Crap Control Freaks around you...I retired after 24 yrs and was told to remove my NOBAMA bumper sticker from my car as it was DISRUPTING MORAL, and they took my clearance and I retired due to it. Sad they are so corrupt and evil.

Being Navy, I am not an authoritative source on this; however, a superior, NCO or officer, can order you, under AR 670-1 and probably other Army regulations, to wear a bra, depending on the overall circumstances at the time and in the place where you are assigned. For example, in Suadi Arabia, Iraq, Afghanistan or another majority Muslim nation, your superior most certainly could and should issue you such an order, assuming there is not already a standing order in place. For example, if you serving as a recruiter somewhere in the San Francisco CA area, there is little legitimate reason for such an order.
Should your superior NCO issue such an order, he or she had damn-well better be in the right and have the backing of the command because issuing such an order could be interpreted to be sexist and scar the NCO's record and service. Whether right or wrong, you damn-well had better follow orders without questions, regardless of how you may feel about such orders. Even if the order is unnecessary, your failure to follow a legal order would be insubordination and punishable under the UCMJ, at a minimum in an Article 13, but possibly even more seriously than that. The fact that your superior is a female, makes her order even less controversial, and is far less likely to be second-guessed by her superiors.

when you join the US military you forfeit most of your constitutional rights. your only job is to be ready to fight and if need be die for your country, Americans citizens and fellow soldiers

In civies on base? YES. Off base-off duty: it would be to accordance of the State Department and DOD while serving in a foreign country.Remember you are also an ambassador to the USA while you are there. Best bet go to your JAG office and ask the lawyers of the military law.

Many leaders cross the line. Instead og consulting the AR they believe that they are the AR.

In my day they could. My favorite line was, "Your mommy and daddy will appreciate the fact that I am not letting their little angel walk around looking like some two-bit back alley gutter whore."

I encountered this at NATTC Millington in 1971. I was told to find a reg requiring the wearing of a bra. I could not find such a reg, but I did find a reg from 1941 requiring the wearing of a GIRDLE for WAC's.

I have actually refused to issue an order like that.

A thought, which a lot of Americans seem to miss when overseas (I grew up in South America, so have sort of an "outsiders" view to a lot of American culture) -- what you consider professional, might be considered anywhere from less-than-professional to downright, well, there aren't any polite words for it -- depending on the local culture.
Remember, here at home or Over There, you are a walking advertisement for the US. Not just the military, but the whole country. If you ignore their customs and standards (no, I am not advocating blanket acceptance of all customs -- no hijabs, thank you!) you make ALL Americans look bad. After all, you are a guest in their house. If you show that you are at least trying to meet their customs, it will generate a LOT of good will.