But lets go deeper. How about we go by examples of people who were disqualified. Specifically people in the 1800's when the amendment was fresh and generally the same people who passed it were around.
Kenneth H Worthy, 1869, disqualified by the North Carolina Supreme Court, never convicted of a crime, appeal dismissed and ruling confirmed.
William L Tate, 1869, disqualified by the Noth Carolina Supreme Court, never convicted of a crime, appeal dismissed and ruling confirmed.
JD Watkins, 1869. disqualified by the Louisiana Supreme Court, never convicted of a crime, appeal dismissed and ruling confirmed.