Having spent 4 years USN, I would suggest you take the course of least resistance. While it may irritate you that they are narrow minded, it will only become harder for you to serve. Wear what they expect while you are a part of them. I do understand your frustration, I am not allowed to wear a kilt to the office because they have an unwritten dress code for representatives and my company helps me live like I want (with the exception of a kilt in the office).

Since this is a military unit, respect the views of your officers and bite your tongue. It may be hard to do but you will be a better man because of it.

Afterwards, put on the kilt and have an "Aquaviit" for me!