Can addressing junior service members by rank alone be considered a derogatory term?

I don't necessarily see anything wrong with referring to someone by their rank alone. However, the tone that one uses may be derogatory. In basic training, one of the nicest drill sergeants called us "maggot." The way he said it almost felt like respect.

I've been told by senior NCO's at my Battery that it's best to call privates by their last names since they don't need to be reminded that they're privates and they prefer to be called by their last names anyway.

Specialist and above I refer to by their rank + last name or just rank for the top two because they're ranks that must be earned: "Specialist Snuffy," "Sergeant(E5-E7) Smith," "Master Sergeant Pricky," "First Sergeant," "Sergeant Major."

WO1's are always Mr./Ms. I do not call them Chief because they have not earned the rank of CW2 and thus the right to be called chief. CW2 and above are Chief.

Lieutenants I always refer to by either their first name or their rank + last name such as "Joe" or "Lieutenant Schmitty." I always ask their preference first and follow by that.

Captains and above are sir/ma'am unless they're with another at which point it's "Captain America" followed by a sir or ma'am in there to show the due deference.

I dislike when people require Soldiers to refer to their status / rank twice in the course of a single statement "sir, yes sir." This isn't the Marine Corps. A single sir, ma'am or sergeant will suffice.

Also, a group of male officers is gentlemen but I also refer to a group of male mixed enlisted ranks as gentlemen (it's too awkward to say "sergeants, specialists, and privates" and ladies / gentlemen will usually suffice.

As last resort I'll just call them "Soldiers" or by the name of their platoon. A group of female senior officerd is ladies. A female and male senior officer of the same rank are ma'am then sir. And so on.

It is possible that people automatically identifying a soldiers rank as derogatory may unknowingly think they are better than the soldier just because they have a higher rank. That would be a false assumption. Your position determines your rank, we all start and end somewhere. Your rank is what is respected, ALL rank is to be respected. In the case of Officers for example it is the rank, not the man, that gets the salute. Soldiers work hard to earn their positions, some aspire to higher levels but not all can attain the top position that does not make them any less of a soldier. Lest we forget we all take the oath to protect and defend the constitution. That is where our inherent respect is earned. Our rank is merely the position we hold for the period of time we hold it. 32 years ago the Sergeant Major of the Army was a private. Did he deserve less respect then? Was he less of a man?

C'mon Lt. this is something I'd expect from a "I'm going to change things A1C" not an officer in the Army. This is the military regs are in place for a reason. Not only that, you have to start from the bottom to reach the top. Meaning you have to take the "poop" that rains down from the top until you make it there. That's they way the world is not only the military. A private is a private not a mister or miss. They gave up that title when they signed the contract.

It's more about the attitude behind what's said than what is actually said.

In the Navy as Enlisted our pay grade is attached to our job. So there is more than 1 way to call someone:
E1-E3 = Firemen, Airmen, Seamen
E4= Petty Officer, or MM3, Shipmate
E5= Petty Officer, or MM2, Shipmate
E6= Petty Officer or MM1/BT1, Shipmate

When speaking to a group of sailors of any rank: Shipmates

no one called me Sr. unless I was wearing street clothes.

I thought this was a duffleblog question I was laughing so hard.

I think you are making a mountain out of a mole hill, and you also could be setting up some of these young soldiers for some pain when they get to their next unit.
I took time to learn every soldiers name within my formation as a battery commander, but the easiest way I can describe how I or any of my leaders talked to our soldiers is how parents talk to their children. They do not always use their formal names, and when they do they generally know that something is up. You build unit resiliency by lumping groups of individuals together and forcing them to work together. There is a lot to be said of the SPC that ran the barracks, not out of the fear, but out of respect and because he was generally a peer of the junior enlisted they listened to him without bitching.
It is similar with Officers. The XO is the leader of the LTs in a BTRY/CO/Troop, but because they are all the seen in a semi-similar light to the commander they are lumped together.

I don't know if any of that makes sense, but I am going to go with it for now.

i dont really consider it disrespectful when other service members call me private

I am glad it refers all SMs in the Army as Soldiers.