All the features of a good military rifle were not applicable to a good hunting rifle.
For instance, military arms had provisions to be rapidly reloaded via some kind of stripper clip. Clearly needed for a soldier in a fire fight. But for a hunter who's target would disappear and not come back if he missed, not so much.
And, that rapid military firing resulted in a hot barrel that could burn hands. And that is bad. Reloading, bayonet/CQB fighting and even trying to find a position that gives you cover and a shooting position could result in burning yourself on exposed barrel metal. So, the barrels were fully enclosed in hand guards. Hunting? Not likely to get the barrel that hot. And you don't need cover; concealment is fine. And you can pick you concealed position so as to provide a good shooting position. A "prepared" position. As a result, the extra weight and potential accuracy penalty of the fully shrouded barrel is not needed.
Speaking of accuracy...The military cares about minute of man out to about 500-600 meters. You don't have to kill the enemy to remove them from the fight. In fact, there is doctrine that indicates a wound if better since it removes not only the fighter, but his buddies that drag him off for aid. So pin-point accuracy for a quick, humane kill is not needed. Either from the sighting system or overall precision of the platform. But a hunter is interested in killing his prey. And the faster, the better. Shot placement is king in that world, so overall precision of the platform is very important, and a sighting system that allows you to use that precision is needed too.
And, what about all that CQB stuff. Not much need for a bayonet when you are after bambi. Yeah, I know there are those crazy guys that hunt hogs with a knife, but that is not the norm. So, the sporting rifle can lose the bayonet mount.
The military needs to size the rifle so the GI's can use it. And a tall guy can use a short rifle, but a short guy might not do so well with a rifle that is just too big. So, military stocks tended to be on the small/short side. And since they put a cleaning kit in the butt stock in most cases, a recoil pad that adjusted length really wasn't an option. Not that they wanted it anyway, since they wanted you to be just as effective with whatever rifle you were handed. But a sporting rifle benefits from being adjusted to the shooter.
And cleaning. No need to haul a steel cleaning rod around in the woods as a part of the weapon system. If you barrel gets blocked that badly, go back to the truck or camp and clean it. That action is less feasible in a fire fight. And you typically don't spend weeks or months on end camping with minimal supplies when on a hunt. But that was a reality for a soldier. And logistically it made sense to put all the needed gun stuff on/in the gun if possible.
I am sure guys smarter than me can add a bunch to this list. And there may be more fundamental reasons for some of the changes. But that comes to my mind right off.