What can be realistically expected, without accurising interevention, so in original condition?
(my guess is 2 moa at best
With each model rifle's issue military issue ammunition for the WWII era, 2 MOA on average is probably a good guess. Some would certainly shoot 1 MOA but on average for a batch of the same rifles with the same era military ammo, 2 MOA is a good guess.
The M1903A3 Springfield in 30 US Government (30-06) had a reputation for being a target rifle among pre-WWII military rifles. I think that most French and Italian issue WWII era rifles might not shoot as good as a Springfield or Mauser.
The older bolt action service rifles had wood protecting and attached to the forward section of their barrels. This is not conducive to rifle accuracy. The triggers were anything but a crisp 4 pound break. Their iron sights were battle tough and designed for target acquisition and quick sight alignment within 100 meters.
Some military rifles with modern hunting ammo, good handloading, or just lucky combinations would shoot 1 MOA. Others might only shoot 4 MOA on a good day. These figures are based on "average" of batches of issue rifles.
Considering that most firefights were and are within 100 meters. During military rifle matches, I occasionally inquired of "experienced" infantry officers how far away they would engage an enemy unit? Their response was always about 100 meters. Anything further they would "call for fire" (artillery or air support) if possible. Something like "Why risk your men when an arty or close air support would eliminate the threat?" was their response to my POG questions.
Considering those factors, and that weapon reliability in a firefight is pretty darn important, along with cost to procure and maintain weapons, 2 MOA is good military rifle accuracy.
The above stated, the modern M-16/M-4 rifles are more accurate than that, especially with standard issue optic sights. Their accuracy is inherent in their design and greatly benefits from CNC machining. Just put together a bunch of AR-15 parts and it will probably shoot 1 MOA or just a little bigger group at 100 meters. At least mine do.