.223 Rem vs 5.56 NATO is probably one of the most discussed and contentious reloading topics ever.
The differences between the two cartridges are minuscule, but important, and the actual answer as to whether or not it is safe to use 5.56 NATO in your .223 rig is; It depends
Ultimate Reloader gives one of the best rundowns that separates fact from myth.
Here is another good, but less technical explanation.
I know when I shoot gallon water or juice jugs the 223 round zips right through.
But when I shoot a jug with some 5.56 the jug has a violent reaction, I had a gallon milk jug jump 4-5 feet when I shot it with some 193 5.56
SIGH
There is functionally no difference between 5.56 and .223. The cartridge is functionally the same. Will some have different thickness case walls? Yes. Will that thickness variance track to the 5.56/s.223 headstamps? No. Are the chambers different? In theory, yes. 5.56 per spec has more leade than .223, and that in theory can reduce max chamber pressure allowing for more powder to be used before kaboom. 5.56 in THEORY has more leade, but in practice, the reamers for cutting the chambers vary enough in their specified dimensions that there is significant overlap between .223 and 5.56 chambers. Add in tool wear and it varies even more. Should you not care? If your barrel was made in the last ~20 years, probably not at all. We aren’t talking about blow up your gun differences here. Be aware of signs of high pressure. If you see them consider not shooting that ammo in that gun.
Popping primers (i.e. the back out of the case or come out completely)? Stop.
Piercing primers? Stop.
Hard extraction? Stop.
Peening away the headstamp? Probably should stop. Depends on how much weather you are risking breaking stuff soon or just prematurely.
Leaving ejector impressions? You are probably wearing out stuff quicker than you’d like. [ETA] IF the ejector impression is smeared, you should probably stop.
If you are reloading, yes you need to worry about more things relevant to case lifespan and safety for reusing them.
Or just do the smart thing and get a .223 wylde 1:8 barrel and not have to worry about your 50-77gr commercial or surplus ammo much.