The US Constitution doesn't prohibit people from running for office while in prison. On the one hand, it helps to prevent the party in power from jailing their opponents to keep from losing power. On the other hand... Well, this.

Since the Constitution doesn't say it, the entire politcal population us entirely too goddamn stupid to do the obvious.

Keep in mind that the constitution was written by people who were all considered criminals, so there wouldn't have been much appetite for being hard on "criminals" in the political process.

Also think on the civil rights reform era. Many of the very well respected figures of history were, at the time, convicted criminals under unjust laws.

Of course, it is inconsistent that in many states a felon can run for office, but can not themselves vote. I would say the weird part is that they aren't allowed to vote.

In short, in a sane world, we should not have to rely upon disqualification to judge a candidate for their crimes. Nor should we have to fear the felon vote, even if they want something unreasonable, they should be drowned out by the more reasonable voters. Even as many folks may currently be on the side of "I don't want that asshole to be able to run", there's a slippery slope from that to having candidates you do like get disqualified owing to unjust laws or application of law.