I'm with you. There are plenty of excellent "MO" marked rifles (SVTs and Mosins and German stuff) as well as handguns. I have several. They certainly were not all old or worn out. The Romanian "Instructies" seem to meet the second rate definition a bit more, but not "MO' marked rifles.
The guessing is fun but hopeless.
I asked the curator of the Tula Arms Museum face to face what it meant -he didn't know, and I asked the staff of the Moscow Museum of the Great Patriotic War and they didn't know.
As you all should know by now, it can't mean "Ministry of Defense" since that wasn't even created or named until 1953.
My own guess, and I mean guess, is that it refers to an oblast issue to local forces such as the Moscow Oblast (the largest), perhaps during wartime guard duty as what we call militia.
These large "worker's militias" did great armed defensive duty at many cities including Moscow, Leningrad and Stalingrad, but were never officially part of the Red Army. Exempted from military service because they were part of vital industries, these workers, men and women, took up arms as required in defense of their cities on many occasions under Army command. The famous Leningrad "blokadnik" bayonets were used by such a force. Postwar in the rubble of the cities such workers groups kept order and perhaps guarded the tens of thousands of German prisoners forced to clean up the damage, needing arms to keep the prisoners at their tasks.
Another interesting possibility is for the legions of special railroad guards who were required to guard ports, docks, bridges, warehouses, tracks and stations in both peace and war. There were many thousands of such armed guards required both wartime and postwar as the USSR had tens of thousands of miles of track and a lot of unfriendly neighbors and bandit partisans in some areas. These uniformed guards were attached to various transportation departments but were not Red Army, sort of like our TSA now.
Another is for training of young people in which the Ministry of Education received both rifles and retired soldiers to train up young students, boys and girls. My wife was part of this training but doesn't recall any "MO" on her rifle!
All guesses, but fun to argue about.