The 14th amendment has barred some people from office. None of these people were convicted of insurrection.

Sure - but different people did different things on January 6th, with different legal consequences. That's why some members of the Proud Boys were convicted of sedition, while Trump hasn't even been charged with it. There's a difference between overtly and directly planning violent physical activity against government officials, and engaging in a conspiracy for election fraud. The former fits far, far more easily into the basked of "insurrection" than the latter.

There is a different level of evidence required. A criminal conviction requires "beyond doubt". A civil action like the 14th amendment has a lower requirement of 'preponderance of the evidence' (i.e. that it is more likely than not).

Which is true, but not a great argument in support of no evidence required. The claim being made is that the 14th is self-executing. That there doesn't need to be any hearing or court determination or process whatsoever by which evidence is presented and evaluated by a judge, whether in a civil or criminal proceeding. That a member of elections department staff can decide to disqualify Trump from the ballot based on what they've seen on the news and in the papers, and without any requirement to give Trump an opportunity to present evidence or argument.

It's really hard to see judges - who generally place great importance on process and an opportunity to be heard - going along with that idea.