What is acceptable accuracy? You might well ask, how long is a piece of string? Acceptable accuracy really relates to the capabilities of the individual rifle and the capabilities of the person pulling the trigger.
No one talks about it much but the stability of the rifle is also important. As an example, it’s no use comparing a 1914 SMLE and a modern-day benchrest rifle. The two are simply poles apart in technology.
In the modern context, there’s the question of the accuracy of so-called entry-level rifles. We have had three within the family, of which two remain. All three were genuine 1.25MOA rifles and often would shoot one-inch three-shot groups.
It was quite different just over 100 years ago. On testing rifles from the factory in WWI, those that shot three-inch groups were put aside for use as sniper rifles.
Quality control of factory rifles improved after WWII but more or less remained static until there was another leap in technology when computer-controlled machinery provided better-quality rifles. Computers also controlled the making of ammunition, for another leap forward in overall quality.
In terms of potential accuracy, the rifleman of today has never had it better.
The other issue of individual accuracy is in the hands of the home reloader who is able to match components to an individual rifle to provide the best accuracy.
Another issue is the sights. No matter how good the shooter is, they’ll never reach the full potential of the rifle/ammunition combination if the stability of the sighting equipment is suspect.
Considering all this, it really gets to the point when we must talk numbers. I must stress that this is an individual opinion based on reloading and shooting a great deal of ammunition in many different calibres.
With quality ammunition, I would expect any modern hunting rifle to shoot at least an MOA three-shot group or better. With both hand-loaded and factory ammunition, you may have to expend some time and effort to achieve this aim, depending on the rifle.
For any rifle up to a .243 that is used to take small targets at long range, I would suggest that the rifle/cartridge combination has to be able to shoot at least 0.75MOA to be successful.