But that implies that, as employees rise through the ranks, there must come a point at which their political stance starts to matter.

We had such an arrangement here in Germany (then West-Germany) a few years back: When you wanted to become a civil servant beyond a certain pay-grade (if I remember correctly, it was the first "advanced" pay grade for schoolteachers) in the 70s, you could not be a member of certain political parties (KPD, the communist party for instance).