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.