Anyone know what Army Regulation (or any branch) that allows a higher-ranking officer to call a lower-ranking officers by their first name?

Yes, here is the regulation: Rank has it's privileges. I was a Sgt E-5 when I left the Marines, I worked for a MSgt E-8 (later E-9 MGySgt). He called me Welling, I called him Sgt. Williams...………….. What was I to do, tell him to stop that? So, a Colonel calls a Major by his first name...…………… go ahead, buck the reality and see what it buys you.

When I was in BNCOC (not sure what they call it now) everyone in our platoon called each other by first name. We were all SGTs getting ready to pin SSG, so no one outranked anyone else. It drove the drill sergeants crazy, and they hated it. But it sure did solidify us as a team.

Not every part of military life requires a "Regulation" or UCMJ Article to direct or deter behavior.
When I was an Independent Duty Corpsman (E-6, two LCDRs told me we could be on a "First Name Basis" - They called me 'Doc' and I called them 'XO'.
When called by my first name or nickname (Duck) by a senior enlisted or Officer, it felt a though I had their trust and respect. I continued this with my subordinates when I was an Officer, but they knew where I stood as a Division Officer or Training Officer... "L -T" or "Doc" was acceptable and they rarely had to use my last name.

FM 7-21-13 chapter 4-6, Customs and Courtesy. Always address lower ranking Soldiers/Officers by their rank, hence the Fraternization Pamphlet and UCMJ code.

I don't see anything with it this, my General use to call me by my first name it made me more at ease and that let me know that he respected as I did him. Now when we where was in mix company or at High Meeting it was my rank and last name. My General was one of the greatest though

First of all first names in ranks is not good. In a squad, office, headquarters, for the superior to address the subordinate by first name (or last name without rank) I found common.

Was common in the Navy for the CO of the ship to use first names. Generally if being Called by rank we had company on board or you stepped into something you shouldn't have. Like your mom using your full name James Thomas Jackson. Gets your attention and you new you messed up something

Back in the late 60’s early 70’s, the USN had a requirement that you meet with junior enlisted and write up a bio. Gave you insight to what was going on with the individual. Senior calling junior by first name ok but not vice versa.

Nope, if you're going to call a subordinate by thier first name at least give them the option to do it back.

If you had more than one person with the same rank and last name how would you differentiate which one you were talking to? At Ft Lee, Va in the Second Instructor Company we had 17 SFC Johnson's. There were three with the same first names. Two had the same MOS's. Confusing, yes but we figured it out. One was married, one was not, They were addressed by rank and first name, MOS, and married or not.It was a little bit tedious, but it still allowed the military dignity to prevail. We never addressed someone by their first names only. That was never done.