Criminal charges should not prevent a person from serving in government. Someone is innocent until proven guilty. It could create a potential situation where political enemies launch charges against one another. Even if convicted, someone has the right to try and rebuild their lives and be accepted back into society.
You could have small criminal charges or even be charged in something you weren't even involved in but that would prevent you from serving the government. Now, what's the point of serving time or punishment if you can't learn and grow from the experience, isn't that the point or is it just to punish the person and hope they don't do it again. Now, I'm not saying a murderer or pedophile should be allowed to serve the government but there are cases where the charges are minor to where it can be seen as a learning mistake and just because they made one or two little mistakes shouldn't ruin the rest of their life.
Criminal charges should not prevent a person from anything unless it is a felony. We have all made minor mistakes and if Making a Murderer has taught us anything, it's that we cannot trust the system. There will always be bias in some link in the chain. However, misdemeanors should be expunged quicker to help good people.
It would be very short-sighted for a single criminal charge in one's past to preclude someone from serving in Government. I think that Government would be well served by comprising people from a wide variety of backgrounds with a rich history - people should not be banned jsut for a crime in their past.