Here in the US, the Amish were not exempt from the draft. They were not, however, required, to serve as soldiers and were assigned to be medics or given some other “alternative service”. Just as mandatory as any other draft, though.
For some Amish, this wasn’t good enough and they went to jail rather than serve the military structure in any capacity whatsoever. Among their communities there a substantial oral and written history of this. Apparently a number of those who served time in jail were victimzed there, which isn’t surprising given their very firm views on non-violence and turning the other cheek. It apparently generated some debate among them, as some were willing to accept alternative service and some were not (since the Amish do not recognize one supreme Earthly authority there’s always some debate among them on proper conduct and religious doctrine)
I expect other CO type religious groups have wrestled with this, too. While to the average person “alternative service” or being a medic or some such might be enough for the CO, to some any support of any war is wrong.
Just in case anyone not from the US or Canada is unfamillar with the Amish and the related Mennonites - they’re a group of Protestant Christians with some very strict ideas of how to live a Christian life. The Amish are a more extreme form of Mennonite, and they have a long history of refusing to fight even in self-defense. Which is why they no longer exist in their land of origin - Germany and Austria and neighboring areas. The other Christian demoninations basically wiped them out, in some cases committing some gruesome acts of violence against these folks who really wouldn’t fight back, even to save their lives.
Living near Amish Country here in the States I can say that, yes, they CAN be annoying at times, but I don’t find them any more so than any other groups with extreme views. At least they don’t generate suicide bombers or airplane hijackers.