"Acceptable accuracy" depends on multiple conditions. I prefer MOA or better for my bolts, 1.5 or better for my levers. Wind adds a whole new layer of complexity where higher velocity and B.C. are your friends.
Well, on a bench I am consistently under MOA. I was referencing accuracy in actual field positions.
Regardless of field or bench, you can never exceed the inherent accuracy of a particular rifle/load combination. I can often come pretty close to (my) bench accuracy in the field when I have time to prepare for the shot and have a solid rest (my pack, a rock, stump, tripod, etc.).
Other than that, I'd say "acceptable" accuracy in the field depends on the results of the shot in question.