And even some activities while they are "off the job." The posted regulations prohibit all sorts of activities, and signing the petition is singled out as "not on company time, but okay on your own time." I take it that the other activities are prohibited even on the person's own time, unless they resign their state classified position.
They might be prohibited from running for offices that would have some jurisdiction over their department, or if they win the office they would have to resign.
"I take it that the other activities are prohibited even on the person's own time, unless they resign their state classified position."
That's how I read it.