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?