Military members can exercise free speech and even participate in political parties and express their opinions, but they cannot do so as a member of the military only as a private citizen. If you first post that you are a member of the military, then you limit your options. The problem this sergeant faces is because he identified himself as a Marine while making the statement. Had he never actually mentioned his being a Marine, then he would of been ok, unless of course he is a Commissioned Officer, in which case there is a UMCJ article for contempt towards public officials. But having mentioned and identfied himself as a Marine, he is then "speaking" as a Marine, not a private citizen. It is a very thin line, and one I would not recommend any member of the armed forces to approach. There are members of this forum who are active duty, if they post with a comment identifying themselves as active duty then express a political opinion, then they also have crossed the line and will and should be held accountable for their actions if brought to the attention of their commanders. However, if they never post that they are active duty members, then they have the same right to post their opinions here as anyone else. Their right to Free Speech is limited, not totatlly taken away.
Also, note that he said he would not follow any UNLAWFUL order, not that he wouldn't follow orders. No member of the service can be forced to follow an unlawful order, even one from the Commander and Chief. There are legal means to get a determination if an order is unlawful or lawful if the question arises. I do admit however, in this case, at least the way it is expressed, that he thinks he would determine lawfulness not the proper authorities, but stating he would not follow unlawful orders is not mutiny or any other crime, even under the UCMJ.
He crossed the line after having been priviously informed of his actions were in violation of existing Regulations and Orders. It is that failure to follow orders that gets him into trouble under the UCMJ. Conduct Unbecoming may also be thrown in there. If he rejects non-judicial punishment, then the commander within his chain of command that has Courts Martial authority could then order a trial. Under non-judicial punishment, he can receive extra duties (limited), reduced in grade (but the amount of reduction is limited), be fined (also limited) and dismissed with a General Discharge, Under Other Than Honorable Conditions, which can be appealed and sometimes are upgraded to Honorable. If found guilty in a Military Court, depending on the level of Courts Martial, it is a felony conviction on your record with loss of gun rights, voting rights and others, he can be given confinement at hard labor, forfiture of all pay and allowences, reduction to E-1 and given a Bad Conduct Discharge or a Dishonarable Discharge, neither of which can be upgraded unless he wins an appeal of his conviction, they allowable punishments is determined by the level of Courts Martial called, but all guilty verdicts of any Courts Martial are a felony conviction. This is not a case which he would want to be put before a Marine/Navy Judge or a panel of Marine/Navy NCOs and Officers.