No, they qualified under the "Conscientious Objector" clause in draft laws (they still have the register for selective service today but if a draft is called they don't have to fight). Their group is part of what is called the "peace chruches" for whom non-violence is a main tenant of the faith, sot they were not conscripted into the army. The US actually has had that policy for a really long time, so sometimes people would join these churches (Quakers, Mennonites, etc are also part of the group) so they weren't forced to join the army. Today you can qualify as a conscientious objector without being a member of one of these churches, you just have to prove that you actively practice non-violence.

On mobile so no link right now but, in my area, near Fort Derrick, MD, Seventh c Day Adventists volunteered to be chemical weapon subjects rather than be drafted. It's been a while since I read about it so I don't want to post misinformation, but they would get mild doses sprayed in their faces at a facility called the 8-ball. I'll see if I can find a link later.

Edit: found a link quicker than I thought I would http://usatoday30.usatoday.com/news/health/bioterrorism/2001-12-20-whitecoat-usat.htm