Other then specifying Christmas, what is the error?
The Klan was purpose-built as a fraternal organization after the war for ex-Confederate soldiers. It has nothing to do with the nonexistent Confederacy or Confederate soldiers in the Confederate Army.
The author later got around to that here: “In Pulaski, Tennessee, a group of Confederate veterans convenes to form a secret society that they christen the “Ku Klux Klan.” The KKK rapidly grew from a secret social fraternity to . . .” To something else.
It is a small point, but why not get it right?