I'm not a military person or from a military family, but it sure sounds like the dude disobeyed a direct order, so jail seems like he got what was coming to him according to military law.
As far as I know, the order was unlawful because the First Amendment still applies to members of the military. They cannot tell him to stop using his right to free speech "without exception".
Otherwise, members of the military would effectively not be citizens. Otherwise, they couldn't run for office (which they are allowed to, but in order to take office, they have to resign). Otherwise, they would have no say on how the country is run because they couldn't even petition Congress to pass laws against actions by superiors. They couldn't petition the courts for relief when a superior did something wrong.
Say a superior sexually assaulted a subordinate. If what you said was true, that subordinate could never tell anybody. That's absurd.
And when I was in, we were allowed to be critical of superiors as long as we obeyed every lawful order.
That's not exactly true, and even to the extent that it relates to real offenses, I think the upthread commenter would be correct that an order to not post to social media “without exception” (barring, e.g., a special mission where that is a bona fide security requirement) is probably an illegal order.
Of course, to the extent that his conduct using social media before or after is insubordinate, disrespectful toward military superiors or civilian officials, seditious, unbecoming of an officer and gentleman, or prejudicial to good order and discipline, that conduct may still be a UCMJ violation notwithstanding the invalidity of the overbroad order.
The fact that they define limits, in fact, means he still had the right because the limits would not need to be defined if the right did not exist for him.
Probably, but that only really is going to matter if and to the extent he is charged with disobeying an order, which I suspect won't be the only charge.
Art. 88 (Contempt for officials),, Art. 89 (Disrespect for superior commissioned officer), Art. 133 (Conduct unbecoming), and maybe Art. 134 (Conduct prejudicial to good order and discipline), though for the last the preemption doctrine would apply to any conduct that actually fell into the coverage of the other articles.
The actual charges that have been announced are being considered (which weren’t included when the article was first posted) include Art. 88 and 133, as well as two different disobeying-a-lawful-order offenses (Art. 90 and 92.)
We can disagree about whether he is guilty of them, or should be punished (I don't think so, considering he is critical of mistakes that lost American lives), but yeah, the military will probably make them stick.
That's one reason I left before I incurred an obligation. So glad I did because I do not have to follow orders that I disagree with.
Edit: Upvoted your comment because, well, you are correct.