To What extent should officers be involved in politics?

Personal opinion, none.

5 U.S.C.
United States Code, 2011 Edition
Title 5 - GOVERNMENT ORGANIZATION AND EMPLOYEES
PART III - EMPLOYEES
Subpart B - Employment and Retention
CHAPTER 33 - EXAMINATION, SELECTION, AND PLACEMENT
SUBCHAPTER II - OATH OF OFFICE
Sec. 3331 - Oath of office
From the U.S. Government Printing Office, http://www.gpo.gov
§3331. Oath of office
An individual, except the President, elected or appointed to an office of honor or profit in the civil service or uniformed services, shall take the following oath: “I, AB, do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I take this obligation freely, without any mental reservation or purpose of evasion; and that I will well and faithfully discharge the duties of the office on which I am about to enter. So help me God.”

Now we could go down the path of privately and personally but that would merely distract one from the issue. You take an oath freely and as a result, you take on an obligation that is larger than anything personal or private.

Lets have a hay day with this one.

Actively serving officers should not express their political views in ways that may cast undue and inappropriate influence on their subordinates and those around them.

O's and E's should vote and refraine from discussing voting. In private is 99% your business. I say 99% because In private you may be planning an illegal activity. I'm not going there. But this is my way of looking at it and it has done me well.