According to
United States, Chief of Naval Operations. "History of U.S. Navy [Enlisted] Uniforms." OPNAV [Office of the Chief of Naval Operations] Information Bulletin.
11 May 1981:
"The 1866 Regulations allowed a white sennet straw hat in addition to the white cover which was tied to the blue flat hat. It was found that the addition of a white cover did not provide coolness but rather added to the discomfort of the woolen hat in warm weather. This was the beginnings of a distinct white hat which would evolve through canvas and eventually the white cotton hat of recent times. To provide unit identification, which was so difficult in the myriad of ships that were commissioned, a hat ribbon specified to be 1 ¼" wide with the command's name in letter was prescribed. Commanding officers were required to insure that all lettering was the same size on all hats. Standardization was also carried through in size dimensions of the white hat and the mandate that all blue flat hats be uniform in shape and color."
This then places the hat on display as being post-war in origin. HOWEVER... we have all experienced CW Era uniform items adorned at a later date and used at reunions, so there is always the possibility, no matter how slim, that the hat IS a CW era hat, with the veteran's command added at a later date.
As for the jumper, regulations called for a white cotton drill with blue cotton cuffs and collar. There is no specification as to the material used for the cuffs and collar other than 'cotton.' Additionally, it was not uncommon for sailors to have their uniforms tailored, or to have new uniforms made by the ship's 'Sailmaker' from patterns kept on board every ship. The fabric for these clothes were to be supplied by the individual sailors, so fabric types often varied. As for the use of cotton denim, it is known that civilian use of such fabric dates back to the early 1850's, possibly earlier, so it is not out of the realm of possibilities that denim could have found its way in naval uniforms of the Civil War period.
While it has been stated in this thread that the jumper and jacket were identified as reproductions, the use of denim in no way makes the jumper any less authentic than others made without. Just wanted to put in my two-cents.