I'm not but my brother was for many years. He had a lot of fun doing it. He told stories of campfires after hours singing period songs and sipping corn whiskey out of flasks.
Different units have varying degrees of authenticity. My brother's unit was a very authentic one. He'd buy clothing made using period methods and materials. In some cases he used actual antique items like his gun, canteen and flask. It can be pretty expensive to outfit yourself authentically. They would not be allowed non Civil War period items. If you smoked it had to be a pipe or cigar as cigarettes were not common at the time. And the pipe had to be of a Civil War era design.
Even the food had to be authentic. Sometimes all they would have to eat would be hard tack that they made from a Civil War era recipe. I tried it once. Not something I'd want to live on .
Other units don't care as much about being truly authentic as long as you look authentic from a distance. The fully authentic reinactors even make sure the stitching is authentic, even stiches you don't see while this group doesn't worry about hidden stitching as long as the stitches that show look authentic.
And still other units barely make a show of being authentic. They wear modern materials like nylon and might even have Adidas on their feet. The latter group is kind of looked down on by the other two.
As I said, my brother had a blast, unless he was sleeping in a leaky pup tent in the rain and wearing soaked wool clothing. He said that could be pretty miserable.
