Some Background First:
Since I retired, I have 1,954 confirmed hogs down. Prior to that I didn't keep any records. I've been varmint hunting now for about 50 years.
I've used a few different calibers over my varmint hunting lifetime, i.e., 222 Rem, 223 Rem, 22 250, and 243 Win. For the last several years I have almost exclusively used 223 Rem bolt rifles. Because of changes in farming practices and overdevelopment in the areas where I hunt, safe shooting opportunities are limited to about 300 yards.
Furthermore, due to terrain and tick infestations, bipods will not work since they limit my field of view and I need to keep from sitting or lying prone on the ground to avoid the ticks. Many years ago, I switched to homemade shooting cross sticks. To enhance performance, I incorporated a lightweight, easily portable sportsman's chair to sit on and shoot off. With two feet flat on the ground, elbows on the knees I can achieve a very solid position. When I'm in the "zone" I can hold 1 moa off the sticks my declining skills due to aging notwithstanding.
Answer to Your Question:
For me, I consider 1/2 to 5/8" moa (off the bench with front and rear rests) the desirable accuracy standard for eastern ground hog hunting. All my varmint rifles are capable of this standard with tailored reloads, some are sub 1/2 moa.
That doesn't mean I can shoot to that level of precision off the sticks. While I try to shoot 2 times a week at the range off the sticks, it took some time, effort, and technique development to become proficient with the sticks. Almost all my range time is spent shooting off the sticks. I'm always measuring and testing myself.
There are many factors besides the capability of the rifle to making a humane shot. First, the wind, mirage, and stability of the field position. Second, the shooter's ability to accurately estimate the range of the shot. Today, range finders have solved a lot of that latter issue. Third, is the hunter's ability to shoot accurately under field conditions at the maximum range intended to take a shot. Also, varmints move around, the height of the hay doesn't always give you a nice clean profile shot like a target on the range. Standing hogs tend to bob up and down requiring timing the shot which can lead to jerking the trigger. Add in the heat and humidity - these are the realities of varmint hunting - it ain't target shooting!
I use a 3 x 5 target area as my "red zone". If I can hit that, under field conditions I can almost always anchor the hog. Yearlings and pups obviously are more challenging due to their small vital area. After many years of hunting and range practice, my maximum effective range for a
high probability mortal hit off the sticks is about 275 yards give or take which covers the vast majority of my shot opportunities.
I suggest that any new varmint hunting make a field target and set it at varying distances and determine if one can hit it. A 3 x 5 card posted on brown cardboard works nicely. It may be sobering to see what you really are capable of in the field.