True, everybody is entitled to an opinion!
However, I specifically remember my RDC in boot camp say that there is no place for open politics in the NAVY. It made a lasting impression on me because I though that this is a free country and you can vote for whoever you like. He said, "it is true, as long as you don't bring your politics passed the quarterdeck." I have never said or done anything involving politics in the NAVY since.
I grew up in a house that was viciously divided by politics, and I have seen what it can do to people, so I guess I kind of understand the NAVY's policy.
Your RDC is correct, there is no place for open politics in the Navy. My RDC told me the same thing when I was in boot camp too.
What yours apparently failed to elaborate on is that I can have a political opinion, as can everyone who wears a uniform. What isn't kosher is someone in the military going to a political rally in uniform, or speaking at a debate in uniform, or attending a political march in uniform. The reason being is by doing so, in uniform, you're representing the entire military and in essence casting the lot of the Navy/Army/et al for one specific campaign or individual. The military as a whole maintains neutrality.
However, it is perfectly acceptable to disagree with any political policy, that's the beauty of our government. If in this setting we choose to discuss and even disagree about different political positions that is ok. The difference is that we are expressing our opinions as private citizens, and we are not representing the government by our opinions. Perfect example is the Navy Times conducting a poll before the last elections asking who they would vote for. Were those individuals wrong for responding? No, because they were responding as an individual, with an individual opinion, not on the behalf of the military.