This is based on anecdotal sources, but I believe both the Amish and Mennonites hunt.
I have known several who did. The trouble with those groups are that there are so many sub-groups that it wouldn't surprise me to find out that one or more of them do not. It seems each little local sect has some strangeness to it.
I have been friends with a 'local Amish' family group for several years.They take care of my Raintree watering system and mow and weed eat my yard.....at the best price in the area.But most important, I trust them to the fullest!
I know he Amish/Mennonites have a multitude of variations, but going to full auto shoots was what I found surprising.