It's not a determination of a crime, but whether someone is qualified to be on the ballot.
After the Civil War, there were a few such cases, and no determination of crime was required.
The petitioner had received a majority of the votes cast in Moore county at the election of April 1868, for the office of sheriff, but upon his offering to qualify before the Commissioners of the county, a majority of the latter refused to allow it, upon the ground that he was disqualified under the XIVth Article of the Amendments to the Constitution of the United States.
The only objection urged to the qualification of the petition, arose from the fact that he had been elected, sworn in, and acted, as sheriff of Moore, both before and during the late war between the United States and the Confederate States. <--- not a crime
More recently, there was Cowboys for Trump
Couy Griffin, who was removed from his office as country commissioner.
From that:
Section Three imposes a qualification for public office, much like an age or residency requirement, It is not a criminal penalty, and neither the courts nor Congress have ever required a prior criminal conviction for a person to be disqualified under Section Three.