Thank you for the information and your question. Although military servicemembers do not completely lose their First Amendment rights to free speech when they join the military, those rights are, and can legally be, restricted. You will see a couple of news stories about a Marine who was in the news in the past few years for the statements he made about the President on Facebook which ultimately got him an OTH discharge
from the Corps.
There are a few Articles in the UCMJ that apply to speech. One Article is Article 88, Contempt toward Officials. It reads, “Any commissioned officer
who uses contemptuous words against the President, the Vice President, Congress, the Secretary of Defense, the Secretary of a military department, the Secretary of Transportation, or the Governor or legislature of any State, Territory, Commonwealth, or possession in which he is on duty or present shall be punished as a court-martial may direct.” Then there is Article 89, Disrespect
toward a Commission Officer
, which reads: “Any person subject to this chapter who behaves with disrespect toward his superior commissioned officer shall be punished as a court-martial may direct.” Then there is Conduct unbecoming
an Officer and also Article 134
-12, Disloyal Statements. Finally, Article 134-53, Communicating a Threat.
So, as you can see, there are plenty of restrictions on what a servicemember can say. It doesn't matter if they do it off of duty and on their "own" time, since servicemembers are subject to the UCMJ 24/7 and no matter where they are. That said, unless the servicemember clearly is making a threatening statement or clearly disrespectful statement against the President or someone senior in the chain of command, they are not likely to be on the radar of the Command as far as military justice goes. But they should still remember they are in the military and there are restrictions you agree to when you raise your right hand, that you must follow.
Please let me know if you have any related follow up questions. I would be glad to assist you further if I can.