It could likely to be a church parish, but, just so you know, I was not suggesting they were trying to change the name so many years later. My research should explain that I thought that it could be remotely possible that since the McBrides were popular then, that it was named that way on the flag as the McBride women or allied family made it. Also, I did notice that there is a McBride Post Office in Jackson Parish. I did notice a 2011 obituary that states, " Mr. McBride was descended from two pioneer families going back four generations in Jackson Parish, LA." This McBride was born in 1922. Below you will see the record (J. T. and John T. are the same guy) of a McBride in the very company that you mention as the Jackson Greys were supposed to go to the 9th LA but ended up in the 12th LA (see relavent thread on this board a short time ago).

McBride, J. T., Pvt. 12th La. Co. M. Federal Rolls of Prisoners of War, Captured Champion Hills,
May 16, 1863. Sent to Elmira, from Pt. Lookout, 5 days ending Aug. 20, 1864. Returned to Pt.
Lookout, Feb. 25, 1865, and paroled for exchange.

McBride, John T., Pvt. 2nd Co. M, 12th La. Inf. En. Feb. 27, 1862, Monroe, La. Present on all
Rolls to April, 1863. Rolls May, 1863, to Aug., 1864, Absent, captured at Bakers Creek, May 16,
1863; now in Northern prison. Federal Rolls of Prisoners of War, Captured Champion Hill, May
16, 1863. Forwarded to Memphis, Tenn., May 25, 1863. Transfd. to Ft. Delaware, Del., June 15,
1863. Recd. Elmira, N. Y., from Pt. Lookout, Md., Aug. 18, 1864. Paroled Elmira. N. Y., for
exchange, Feb. 25, 1865. Exchanged James River, Va., _, 1865. Roll of Prisoners of War, C. S.
A., Paroled at Monroe, La., June 14, 1865. Res. Jackson Par., La.

http://www.thepineywoods.com/JMcBrideDec06.htm is a short history of the McBrides in Jackson Parish. All of this leads me to the dstant possibility that the flag was made from the community and/or its popular residents.