The Church of Christ/Christian Church movement of which Alvin York was a member before WWI had strains of pacifist/conscientious objection doctrine even before the 1860s. David Lipscomb, founder of Lipscomb University in Nashville and a southern sympathizer, plus other prominent Tennessee ministers, were well-known proponents of this view during the 1861-1865 war and preached non-participation. Many York surnames are on C of C/Christian church records in the area north east of Nashville during that period. Although Alvin York's linage and family religious background previous to WWI is not well documented, it is possible that his family was familiar with pacifist views long before the advent of those post war, disallusioned Methodist ladies you postulate.