A draftee could apply for 1-O status if they could prove that serving in the military went against their religious or moral beliefs. With 1-O status your were excused from military duty, but still required to do civilian service. During the Vietnam War, this status was rarely granted.
A conscientious objector (CO) is an individual following the religious, moral or ethical dictates of his or her conscience that are incompatible with being a combatant in military service, or being part of the armed forces as a combatant organization. In the first case, conscientious objectors may be willing to accept non-combatant roles during conscription or military service. In the second case, the objection is to any role within armed forces and results in complete rejection of conscription or military service and, in some countries, assignment to an alternative civilian service as a substitute for conscription or military service.