Requiring a conviction in the first place is the special treatment I'm referring to.
Disqualification is not a criminal penalty. If it were then it could be removed by a presidential pardon.
Instead it can only be removed by Congress--a body that is specifically prohibited from passing laws that set or alter someone's criminal liability.
Congress can only remove the disqualification, they can't impose it.
It's a problem that the amendment doesn't tell us how it's supposed to work, but the fact that other disqualifying factors (age, residency, etc.) are determined by the states suggests that the states can determine disqualification on the insurrection factor too, and through the same procedural mechanisms.