Proper sling technique will not affect most bolt action rifles negatively, as the sling rides along the back of the support hand pulling the stock directly back into the shooters shoulder. The reason why sling technique is important with a Garand or M1A, or rack grade M16 or M4 is that the sling attachment is either directly on the barrel, or on something wrapped around the barrel. On those military rifles, the sling changes the "pitch" of the barrel harmonics, and if sling tension isn't consistent, groups will open up. Many old shooters found that groups would tighten up going from a rest to the sling because the sling dampened harmonics just enough to be more consistent.
One of the reasons why AR-15s dominate is that a NM free float tube eliminates any sling induced harmonic changes in the barrel. But like I started with, pretty much any synthetic stocked bolt action rifle, no matter how flimsy, is going to be just fine with proper sling technique. Improper sling technique is anyone's guess.
FWIW I earned my Rifleman patch with a 232 out of 250 using a bolt action rifle with 5 round mags. I wouldn't want to try it with smaller mags, but two five rounders wasn't a hinderance.
Jimro