As always, while searching around the Internet for interesting tid-bits, I came across a nice Website for Christian reenactors. It's quaint and seems to be well-maintained, drawing a fairly large readership judging from their "virtual battalion" roster.
I couldn't find anything similiar for Jewish reenactors, but there is a site that does highlight the soldiers and offers a database of those who served in the Civil War. It's very interesting! Maybe someone will step up and do a site devoted to Jewish reenactors.