You're not supposed to be using state resources for personal or political purposes. It's that simple. Any professor who doesn't understand this has no business working for a public university.
Addendum: Here is my university's policy:
D. Political Activities
If you are an employee of the University, you may engage in political activities, but not during your work-time or with the use of state resources. Students are similarly restricted from using state resources when they engage in political activity.
On the other hand, incidental personal use of such resources as email and internet access is not considered a misuse of those resources.
There is no provision for incidental use of state resources for political activities.
Keith Burgess-Jackson, J.D., Ph.D. 