How do you handle a disrespectful junior soldier that doesn't belong to you?

You have his name and rank?
Call Post Locator.

If identity is in question, that would be a concern for the Provost. On the issue of respect, that is something you can not demand however the uniform and rank deserve a certain amount of decorum. It is doubtful he learned this behavior at his unit and they probably have their hands full with him or her too. Probably would love to transfer him to your unit. Ha ha. Obviously this troop is not going show you any more respect by ratting him out like a little bitch so maybe by trying to reach this person and his problem may help rather than kicking someone when they are down. None of us is perfect including superiors. On more than one occasion I, we, in the company would deal with out of control NCO's in the company harassing troops after becoming highly intoxicated by mid day and on duty. This would upset the barracks for weeks and fill the whole company with dissension. Words and action matter and have consequences. Of course there is only so far you can go and an ass kicking is still on the menu. Hmmm! I'd try the get in his head, I don't know where he's been or how he got to where he is at now.

ALCON - I hear what everyone is saying on this thread and while unfortunate, there are those bad apples out there that spoil the bunch regardless of rank and position. If you are an Officer, you already have the upper hand on any EM (at least from a regulatory perspective). If you are an NCO, then anyone lower than your grade and or position can be put into check through the use of regulatory compliance. Remember, to lead isn't just through knowing your MOS/AFSC/Rate/Etc., you need to know what the regulations say; the MCM applies to all branches universally! Unfortunately, many leaders have forgotten that leading by example involves following the regulations (as closely as possible, but remembering to use common sense, grace, and forgiveness when necessary); sometimes, they can be gently reminded if your approach is professional and tactful for which they comply. However, those that don't care and are only there for a paycheck, title, or rank will probably be the ones who cop an attitude and go off on you; with them, just do your part professionally and let karma take its course. If you have subordinates, teach them the right way of leading, give them scenarios, have them do the research to find the answer, cite their sources and then reward them appropriately for their efforts. I hope that this helps!

Doesn’t sound like he has ever been in the military. Pretender comes to mind. Not even a stolen valor case. At least they try to pretend they are something better than they are. This guy was displaying just what he is, a disheveled angry miscreant.
In general, for real military personnel, I would let their command handle it. If I know their command I would tell them what I’ve witnessed if it’s egregious. This one, maybe report to law enforcement and bring charges. I’m pretty sure that’s a punishable offense under UCMJ and if he’s a civilian they should remove him from the installation.

You should have called the MP

I have commented on several others comments. Now for my own.

If said douchebag was off post AND was in the Army (and it is really sounding more that he was not, maybe he was JROTC?) you would get your ass in a crack providing the "behind the barracks" discipline.

In general, people in your command know enough not to play that game. Someone in another unit may not, and that is where tact, or lack of tact comes into play.

Tact is getting name and unit and reporting the incident, and requesting to know what actions were taken.

Lack of tact is the "behind the barracks" solution. And I don't really understand why this cannot occur in today's Army. it wasn't supposed to occur in my day either, but it did. And sometimes that type of corrective action makes for a better soldier, even if it is out of feal that his (her) butt may get whopped again.

Sorry part 2. But to pull that BS, call the closest military law enforcement.

In all my 56 years of being in our around active or non active. Never had to deal with it, even when I made E-5 PO-2 and ran the line shop, but everyone one of us were smart asses and we dealt with it.

In this world we are living right now we have to many important issues to tackle. Let KARMA take over. He will find someone to correct his attitude and guide him to the next level.

If I couldn’t get I’d to include unit from him I would have him detained with my people. Then get protest martial people involved and we will find out all about the person. When their CO was located inform him of what happened and ash him what he was going to do about it. But it wasn’t then nor now that hard to find out who a person on post is. Especially on today’s posts.