As noted above 5.56mm NATO US military brass and .223 civilian brass are for all intents and purposes identical.
Consider something like BHA's red box loads where you'll get 50 rounds of mixed military and civilian cases in what is obviously the same production lot with no special sorting prepping or charging of the cases. It generally shoots as well as cases I've hand prepped and more to the point if you sort a mixed box and chrono them in two groups (military and civilian), you'll get very similar mean velocities and standard deviations. In short, it makes zero difference.
Foreign made brass, and in particular non NATO standard foreign 5.56mm brass is something else, so proceed with caution.
7.62mm NATO brass versus .308 Win brass however is a different story, particularly non-match brass. 7.62 NATO brass was made with thicker side walls to provide more strength and reliability by reducing the potential for a head separation in fully automatic weapons with 1) barrel systems where the head space can quickly become excessive, 2) cyclic rates and extraction forces can be very high, and 3) chambers can be very rough or dirty. Pulling the head off a case and leaving the rest in the chamber not only creates a jam, but it effectively takes that barrel out of the fight. Consequently 7.62mm NATO brass is thicker with less internal volume and you will want to back any starting load off by 10%.