Somebody needs to tell the Gettysburg visitor center that the souvenir hats they sell didn't come around until 1872. The crossed rifle pin didn't replace the gold bugle as a symbol of the Infantry until after the Civil War. Also, insignia was on the top of the hat in the 1860's, not on the front. Insignia on the front was for officers only.
If you see an adult reenactor wearing this hat, scold him sternly and slap his wrist. If he argues with you about its "realism," give him an uppercut to the jaw and tell him to go watch Glory.
Kids wearing the Gettysburg kepis are understandable, because only they make hats that small. But if you see a kid reenactor wearing this hat, pay 2 dollars and get him a bugle pin to put on it, and throw away that crossed rifle nonsense.
Per 1863 regulation, the top of the forage cap or kepi could only have a Corps badge made of wool material or an infantry bugle, the Regimental number in brass, and a company letter.
The brim of the hat was a single piece of leather, not whatever that faux sewn plastic leather they use is. Creased hat brims didn't come around until the 20th century when baseball players folded the cap to put in their back trouser pocket.