My thoughts and opinions on the accuracy potential of semi-auto rifles:

I shot service rifle competition for years with M14s and M1As and I built a number of Garands for competitors in DCM matches back when bedding and metal work wasn't the problem it is in CMP matches.

The match grade M14s and M1As would all hold at least 1.5 MOA 10 round groups with M852 match ammo, (but all nets were off with the newer lots of M118). Mine would hold 1 MOA with tuned hand loads. A NM prepared M1 Garand with a match barrel would give similar 1.5 MOA accuracy with good lots of M72, and most would improve on that a bit with tuned hand loads using 168 gr SMKs.

I eventually switched to an AR-15 and, with a heavy match barrel, a free float handguard, NM sights and a good trigger, it was also 1 MOA capable.

I've also built Varmint ARs with bull barrels that are sub MOA capable.