When is calling a fellow service member by their first name acceptable and unacceptable?

It all depends on the environment you are in.  If the people you work with call each by there first name, that is fine, you can to.  However, if an outsider comes in to your environment then you must show Common Courtesy until otherwise  directed.  If your work environment works well that way, then go for it.  Officers call each other by their first names all the time.

All depends on the circumstance.
IMO.....the military is different from civilian companies in the fact there seems to be a greater emphasis on top-down & lateral discipline.
On the other hand, certain situations tend to lend themselves to a preference or even a need to employ first name protocol.

I'm "old school" and don't think first names should be used when conducting official business.

It honestly comes down to personal preference and what is acceptable within your specific section/unit. At my previous base most people only found it acceptable to be on a first name basis outside of work. With only a handfull of people calling someone else by their first name while on duty.

After recently getting to my current base I found that things are a lot more relaxed here. With people being on a first name basis at work a lot more common. I personally prefer to stick to last names if you're in the airman tier of ranks. NCO's and above I stick to rank plus last name unless told otherwise. The most informal I've been with a NCO is last name only, and that was because they recently put on rank and told me it was fine to call them by last name only unless around people not from our shop.

I personally don't have a problem with people calling me by my first name if they feel like it in a work setting. I've had quite a few Airmen, NCO's, and SNCO's call me by my first name at work but they always checked to see if it was ok first. Although it's largely an Air Force thing, you won't see it much in other branches.

I'm a civilian as well so I get called by my first name all the time, sometimes it slips and I hear random ones call me by my first name as well. It doesn't personally bother me, but I also feel that it is a respect thing. You can tell which ones respect you. I just tell them to watch who they do it around, because it does bother other people. If t were being done in a disrespectful manner, then I would correct it. I usually don't have an issue though. The other civilian I work with, I call by his first name sometimes (try to keep it just during normal work) and rank on drill wknds

Within our command as long as as I am surrounded by fellow E6's we use first names and I am aware that Chiefs and above do the same. However if we are around E5 and below we use titles.

That is the difference between military related tech jobs and AGR.

For example, I used to work ADSW on YTC. Near the armory where I worked, there was a MATES facility, and I came into contact with people from the facility regularly. Reserve component service members who worked there as techs for their full-time jobs were less formal at MATES than they were at drill and AT.

Take it as you will, that just tends to be the norm in that setting.

SSG Philip Cotton, I've worked in places (doing very low-speed work at a very high-speed place) where as an E4 everybody else -- E6's and mostly E7's -- were on a first name basis with me and each other. I could have been an E1 and it would have been the same. When I first got there, they wanted parade rest, but after a day or so all quickly told me to stop doing that.
Most people want standard military customs and courtesies, but in some situations and unit cultures, some people prefer things to be more casual.
I would never address someone who outranks me by their first name, unless and until they specifically tell me to, and even then I tend to be reluctant.
It seems strange even to address or be addressed by my peers by first name. Last name is a strong habit.

I have done it with peers of the same rank but up or down no. This is however more common in the Air Force. While I was in, I called my Team chief by his first name, the pilots all used first names or call signs.

Instances in which I heard it was acceptable to use first names is when a senior is addressing a junior. But I've rarely heard NCO's use first names.

First names are never a good idea while on any active duty status. Rank and last name maintains good order and discipline regardless of scenario. First names start the slippery slop of friendship in the workplace; which may not be a current problem, however, situations are fluid and can change rapidly and friends can find themselves in a subordinate status quickly.

Sgt Cotton, aka Mr. Cotton,

As you settle in your new workforce environment, you will also discover certain organizational norms, nuances and acceptable behavior. This is your leadership challenge. It is for you to decide because of your duality.

When I went and worked AC/RC for a few years, I still addressed the MilTechs as Mister or Misses Last Name during the week and by their rank during drill weekends. It was easier for me as I met most of them in civilian clothing when I met them. So, calling them by their first name should be reserved for outside the office in social settings, if you choose to socialize with them. I had a Maj. at one of my assignments who would call me by my first name, but I always addressed him as sir or Maj. ... this way I would not make the mistake of calling him by his first name in the wrong company. I guess he felt more comfortable addressing me by my first name as we were about the same age.

I would stick with rank while at work and drill for the simple you will slip up at the wrong time in front if the wrong person.
Not worth it

Working in a civilian setting, it really should be Mr. Cotton.  I know that modern society has dropped much of the formality, but that really is the polite and respectful thing to do.  First name basis should only apply outside of work/duty, and should never be to the degree of compromising the integrity of the chain of command.