I don't know what point you are making here. So as not to be accused of ignoring it, could you please clarify it for us?
I guess what I'm getting at is as long as I don't associate my views/opinions with the military there shouldn't be a problem. The same, I am willing to bet, is the same with any other employer. As sad as it may sound if you were to go to a political rally wearing a work uniform you run the risk associating your views/opinions with your employer. That is something that most employer I would like to believe would like to avoid.
A similar but not exact example would be that woman that got fired for the picture she posted of herself throwing up the middle finger and acting like she was screaming next to the sign at the Arlington nation cemetery.
I don't know if that explains it or not. I guess I'm just trying to say its no different than any other employer. The military is just a little more liberal in enforcing such a rule. Hope that helps.