Disrespected while correcting a Soldier, how would you handle this situation?

Calmly tell the civilian that this was a military matter, if that did not work, ignore the civilian, as you do not work for her, nor are you answerable to her. Second, as to the Soldier, was he the one being Courts Martialed? If so, he has to face the judge out of uniform, which will definitely not go well for him, as for the disrespect, nothing is stopping you from formally counseling that Soldier, asking for his his unit or other lawful actions, including and up to notifying the MP's, depending on how the soldier would escalate the situation.

You definitely have at least two violations of the UCMJ, disrespecting a NCO, and failure to obey lawful/direct Orders.

Being of sound mind and body, apparently, said soldier being court martialed was not of sound mind. Also, being a full time civilian and part time soldier, I have a different view interspersed with the memory of being a full time soldier. That view says that yelling is pointless if the person you are trying to communicate with is not affected by your tone. Respect cannot be ordered, it must be earned, and yelling, regardless of your rank, is more likely to lose respect, than earn respect. Why was the soldier being court-martialed?

Are you an NCO ? If so then you are in violation for not doing your job. Was the other soldier in custody ? There are a lot of scenarios that could have taken place there. Generally as an NCO you should have pulled this service member aside and immediately put him at ease then made the correction if he did not adhere then counseling is in order.

I had to read this posting twice, so forgive me as my time in the military was long ago. The soldier reported to his court-martial dressed in fatigues (ASU and ACU are new terms to me)!? If I understood correctly, this soldier had and has a problem you were addressing, and that civilian didn't need to butt in.
What was the outcome of the court-martial?

While DROSing at Dix in the mid 80's I came across a similar situation. A young female PFC was filing my transfer paperwork was wearing a gold cross on the outside of her fatigues. I told her while I respect and appreciate her faith, she needs to place the cross under her shirt as it is not part of military issue or uniform. The immediate indignant look followed by "you looking to get your paperwork lost, Staff Sargent"? took me back. I ignored the comment and proceeded out. I then located her First Sargent and explained the situation. He said "oh that's just how she is, besides, this is clerical job, its not like the real army your in". All I could say was wow, did you a First Sargent just say that? I said thank you and then proceeded to my next duty station in the "Real Army".

I have to assume the disrespectful Soldier was the subject of the Court-Martial? If so, it seems pretty obvious to me that you let the court handle the SM, and if that doesn't work out - you have the Paralegal as a witness. You then go to the CoC and start NJP.

How about informing the rest of us who weren't in Army what ACUs and ASUs are?

At his court martial? what else do you think you can do to him a counseling statement for being out of uniform? If you have already done your worst to some one i.e. Court Martial you really don't have anymore stick to use on them do you? It is silly to threaten them further. So you need to take another tack (sailing term) with them. Also consider this YOU are his ENEMY you are trying to DESTROY this person in a Court-Martial if you want respect you should look somewhere else this may just be business to you but to him it is not.

Oh, and as for the civilian, prior service, look at him in his eyes and tell him Togo back to his office and stand by for a corrective dicession. Get his immediate supervisor and ensure the point is made hat a civilian needs to stay out of military matters while in a military environment, or go find a new job

I don't know the MOS specifically of the poster but, I assume with a paralegal assigned you're an attorney and thus, familiar with UCMJ and it's implementation. The actions of the SM were not silent insubordination but overt, screaming loudly, outright insubordination. I would have instructed the paralegal to hold the SM where he is using any means necessary and called for the MPs (non-infantry types don't usually do wall-to-wall counseling) and had the SM handcuffed and arrested on the spot. Overt disrespect to any officer is punishable by UCMJ (you probably know the relevant UCMJ sections better than I) and in a corporate environment such as a court house is best handled by the legal process (when non-combat arms personnel are involved). Make no mistake about it Marines, Army combat arms NCOs still handle problem children appropriately. But, this was a different environment and JAG officer, never go into a correction mode with any soldier unprepared to use the necessary force to ensure compliance with your orders. This is the Army, not the Girl Scouts. You have to be able and ready to enforce any order you give otherwise, never issue an order you know you cannot enforce or will be followed.