How can your job be to both implement policy set by the politicians currently in office (presumably decided by their political philosophy) without regard to your own opinions and also to not espouse a political philosophy?

The same way that Eisenhower served under the Democrats FDR and Truman then was elected to the presidency as a Republican?

It's a job. With particular job duties. You do those duties regardless of who's in charge. It's just that under one administration those duties are oriented to a particular larger purpose, while under another administration they are oriented to another particular larger purpose. That still doesn't change the vast majority of jobs, and for those few it does, aren't most of them political appointments already?

Implementing a policy and personally advocating (in speech) for a political party line are two different things