Anything that changes/affects the way the rifle moves during recoil will have an effect on accuracy.
Case in point; 6 years ago at an elk guide's place in Colorado, one hunter was having serious problems getting his scope dialed in. This was a 338 Win mag borrowed from his buddy and it was kicking the crap out of him. I watched him closely and he didn't seem to be flinching even though he was getting pounded. After about 1/2 box of ammo, I noticed the sling stud was contacting the edge of the metal rest on the shooting table on some of the shots. When I watched even closer, the shots where the stud hit the rest went about 3" higher on target. Resetting the front rest allowed him to put a good 3 shot group on the target that satisfied both him and the guide.
I used to have sandbags made from old shot bags and could only get good groups when the stud was well forward of the bags. I now use bags with a channel so the stud can't contact the bag.