Obviously you never studied constitutional law. Any law that limits free speech must be "Narrowly tailored to serve a compelling state interest." The blanket rule against expressing political opinions is neither narrowly tailored nor necessary to serve any compelling state interest.
If Congress needs to limit free speech in any context including the military, then it needs to state what the compelling interest is and to show that the rule it has adopted is as narrow as possible to serve that compelling interest.
You're right. I was never in the Military, but I am a lawyer. So you stick to what you are a professional at (which I suspect is following orders without question) and I will stick to what I am a professional at (which is questioning authority and insisting that Congress follow the restrictions given in the Bill of Rights).