Exept the 14th Amendment doesn't require a conviction.
This was intentional because the decision was made to grant amnesty to everyone who fought for the Confederacy, but they still didn't want these people showing up in Congress.
Except the 14th Amendment, article 3 speaks to “.., shall have engaged in insurrection or rebellion against the same…”
In the case of the confederacy, there was an explicit announcement of rebellion against the government.
Nothing in the 14th amendment speaks to partisan Secretaries of State unilaterally deciding upon the exclusion of candidates on election ballots based upon subjective interpretation of insurrection.