Is it appropriate for department administrators to send political emails?
In your question, I note two (different) items:


Sending political emails
Embedding an opinion


Sending political emails

I can certainly imagine that a department administrator needs to send political emails: there are often political situations that have a certain influence on a department/school or its students and staff (e.g. a new law or decree). In general, I believe that messages sent to mass email addresses should be used to provide information that is applicable to all who receive this message. As a guideline, therefore, I believe that such email should be without any opinion.

Embedding an opinion

I believe that personal opinions and emotions should be dealt with in personal circles, and not be shared with the general public over mass email addresses (there are public forums, but then viewers have a choice in reading or not reading). The sender does not know what these emotions brings about with the receivers: it can have significant consequences for people who have dealt with similar personal difficulties. And, strong opinions can cause strong reactions, again with possible negative consequences for the sender as well as other receivers.

As such, I think this behavior should be addressed. Many universities have an Student Ombuds Office, where any issue about university policy, bureaucracy, and conflicts can be discussed confidentially. If it bothers you, contact them, and then they can guide you further and inform you about the university staff member breaching university policies, for example.

Of course, an administrator may also have been asked to inform students and staff of the institutional opinion. This most likely means that a (board) meeting has resulted in a decision from the institution, which is then passed on to all involved in the institution. These messages describe the position of the institution on a certain question, but most certainly exclude emotional descriptors.

In short

The staff member's behavior could be against policies the university has set for mass email usage (using it for both political reasons as well as personal interest). Check the policy for this, and use the Ombuds Office for further advice and guidance on what can be done.