Yes. When a person is convicted of a felony - depending upon the position, denying them employment makes perfect sense. That being said, I would like to see a time limit placed upon that stipulation. For example, Felons serve time in prison. Upon release, they are indoctrinated back into society under the supervision of a parole officer. That can last five years. Once that period is up - and they have demonstrated their positive behavior within society, the stipulation should be lifted and they should then qualify to work anywhere as well as vote.
I believe some people can be rehabilitated. Those that cannot, usually demonstrate that within a five year period.