Just because military brass is noncorrosive don't mean it's not reloadable.
Odds are the issue is Berdan primers instead of the Boxer primers most US reloaders are used to.
If you look inside the case (look at the photo of the CCI Blazer case above) yo usee two pinholes off center, these are Berdan primer flashholes. They put the anvil of a Berdan primer on the case not in the primer cup. Thus the holes have to be off center on either side of the anvil.
Berdan primers are chosen by the military since they don't need to reload their ammo, it's disposable, and the Berdan system is supposedly slightly more reliable in ignition versus Boxer. (or so I've heard) But it's harder to reload, by getting the primers out. It can be done with the right equipment and if you can find the right size Berdan primers. I'm told there are people who are converting Berdan brass to Boxer but it's long and tedious and best reserved for calibers you can't find any other brass for.
There is Boxer-primed non-corrosive ammo out there. In 7.62x51, the 70's Indian (OFV) is noncorrosive and boxer primed, as is the FNM headstamp I think is Hirtenberger. There are more- those just jump out of my mind right now.
The reason a lot of military stuff is corrosive primed is because corrosive primers have a much longer stable shelf life than noncorrosive primers do. I've shot corrosive stuff from WWII that shoots just fine.
The only real issue with corrosive ammo is you need to make sure to flush your rifle out with Windex or hot water or some other solution to neutralize the salts in the priming residue which will rust the gun. Truthfully I've seen 100-year-old military rifles that ran corrosive all their life, brown bores, some pitting, but corrosive is not gonna instantly rust the rifle to a pile of junk overnight. Might not be the best thing to run on a gas operated semiauto, though.
Once you clean and reprime the cases with modern primers, it's not corrosive anymore.
Those "non-reloadable" Berdan cases are worth good $$$ at the recyclers as scrap brass. Don't just throw them out.
Some military brass has crimped in primers so they don't fall out and jam up a machine gun. They just need reamed out to be reloaded easily. If you look at the primer you'll see the metal is dented in around the cup. That's the crimp. Sometimes it's three little dings.