Minorities can, and should be depicted, end of story. To do anything less is a disservice both to the men who fought to make the United States a nation which believes that all men are created equal and to the claimed educational mission of reenactment.
There is nothing wrong with portraying a Muslim, Jewish, or other historical denomination of person. There is nothing wrong with having a mature discussion about how different faiths existed during the war and discussing how faith shaped peoples views of the war. And there is nothing wrong with having a reenactment or group dedicated to reenactment of a different faith than your own.
Personally, I dislike all religions. But the war had a strong religious component and to ignore it would be silly. Ignoring other denominations is equally silly.