I think the flag shows crossed rifles, similar to flags shown here for the 26th division in 1931.
http://tmg110.tripod.com/usarmyh3.htm
If the picture was taken in May of `41, the 181st was still part of the 26th ID which at that time was a "square" division, meaning it consisted of 4 infantry regiments, 101st: 104th: 181st: & 182nd. When the army reorganized to the "triangular" 3 regiment division, the 181 & 182 i believe were assigned to the Americal Division and the 328th was added to the 26th ID.
During this reorganization, some men were transfered out of existing units to fill out new units being formed, MP companies among them. I doubt that a whole infantry company was redesignated as an MP unit in 1941. MP`s were selected on various criteria, being tall was one.