Sure, but almost every state blocks it for the duration of your time in prison, at minimum. A fair portion are longer, and some states make it almost impossible for federal felons to vote.
https://www.brennancenter.org/our-work/research-reports/can-...
> Our current president is a convicted felon.
That’s federal, which has no barriers. It’s left up to the states to decide how state level offices work, and being a convicted felon is a knife in the back of any potential political career. In NY specifically (where Swartz lived) you need a “Certificate of Good Conduct” or else you can’t run, and it would have taken (assuming he got convicted with 7 years as was threatened) 8-13 years for him to be legally able.
The exact specifics don’t even matter for Swartz’s case though, because for him it was more ideological than practical.
This is left up to the states.
> you cannot hold public office
Our current president is a convicted felon.