Being convicted of a crime doesn't disqualify anyone; people have run for President from prison. And most of the people who attacked Congress on Jan. 6 would not be disqualified for it even if they are convicted of a crime for it.
Disqualification is not a criminal punishment. It's not a crime to be 34 years old, for example, or to have been born in another country. But those are still disqualifications, and they are and always have been enforced by the states.
This will be challenged in court and almost certainly be struck down on 1st amendment grounds. Targeting a specific organization like that is a pretty flagrant violation, but I wouldn't expect the supporters of this bill to be familiar with the US Constitution.