FALSE. For a claimed Vet you are very unfamilar with the UCMJ.By the way the oath we take when sworn in to the service of this country DOES NOT contain the phrase that we can't "bad mouth" the commander-in-chief or any other officer in the service. Ask all of the officers that have been relieved of duty because the unit they commanded "Bad Mouth" them.
Article 134, known as the catch-all article, makes criminal those acts of speech that are prejudicial to good order and discipline or that could bring discredit upon the Armed Forces. This is pretty broad and explains why it is often called the catch-all article. If your chain of command thinks your political involvement has affected your unit or the military, you could be punished under this article