5.56 Nato is "military" and has to be made to specific "mil specs". .223 is made per SAAMI specs. Mil specs and SAAMI specs are not the same. 5.56 Nato will fire in a dirty firearm. They also have crimped in bullets and crimped in primers to seal them.
I am a member of a LARGE shooting club. Many of the guys shoot the military matches with old military mausers, garands, etc. They also shoot M15s, M16s, ARs, etc. One month they will be shooting groups with military or surplus ammo. Next month or big matches they will be shooting their reloads with commercial brass.
The main thing here is to know your gun and know your ammo. I won't beg, buy, or borrow someone elses reloads to shoot in one of my guns. I also will not shoot ammo I am unfamiliar with in my guns.
My .223s have seen lots of Remington, UMC, Winchester, WCC, PMC, and Federal ammo. I also have hundreds of reloads using this same brass. This is mixed military and commercial with no problems. None of my guns have ever seen steel cased ammo. I know nothing about it. I am also very picky with military surplus from outside the country, unless it was made by, or for, the country where the gun was manufactured or used. I have several military rifles and use the original military ammo made for them. With these, the concern comes with the commercial. I have to read up on it before I can use it.
Know your gun. Know your ammo. Shoot safe.
Steve