The Trump military tweet? He's commander in chief. The pentagon reports to him. That's an important point. How to interpret it's a bit harder.
When Obama scrapped the don't-ask policy, there was a law in place by Congress banning gays from serving in the military. And the ban didn't immediately lapse. In fact, Obama had to certify that adequate review had been taken to change the policy. (IIRC, the original law was put in place because of fears that the Clinton administration would change the policy. That sort of entails that the policy wasn't law until then.)
I don't recall any law being passed rescinding a ban on trans citizens serving last summer. It seemed that Obama announced it in consultation with the military. He would have had to sign off on it as commander.
So while Trump can't tweet away the law, it's far from clear (and looking pretty good) that there's no law governing the policy itself.
The new trans policy put in place last year was written by an undersecretary of defense (according to newspaper accounts Google kindly pointed me to). Not by the chiefs of staff. It was pursuant to review that the DoD said it would be carrying out, but that sounds like an internal decision. Are there procedures that Congress put in place for revising military policy? No clue. Nobody's said there were any. I'd have thought that would have been the first thing shouted out. But it may be buried in the arcana and esoterica governing the military.
It will certainly be contested in the courts, if only because Trump said it (if he said that the sky was blue or that hydrogen typically had one proton in its nucleus, at least 3 cases would be filed in three different circuits contesting it). The most likely grounds will be sexual-orientation discrimination. If those currently serving are dumped--for which there is no policy, regulation, law, or precedent--that suit will certainly succeed because it will be breaking a contract. If the policy is just no longer admitting trans soldiers, or admitting them while requiring that their biology remain unchanged for the duration of their service, that's far less clear, unless the courts decide that they're now in charge of reviewing what military and political folk think is "appropriate" and required for military readiness and coming up with their own definitions for the terms. The courts have shied away from that in the past.
Reading Trump is an art, but like all art you have to go in open minded and inquisitive while most people before they even read what's said already know they'll disagree and it'll be as bad as it can be.
That said, I suspect the policy he's getting at is probably the latter. Currently-serving personnel were to be trained on policy and procedures and such by 7/1/17, with openly trans recruits first admitted as such after 7/1. That was delayed pending further "review". That policy could be easily reversed without affecting anybody except people who hoped to join the military. (I know at least one trans Army recruit, but apart from a haircut, as of the last time we talked he was completely female apart from a moderately butch haircut--one that wasn't exclusively male, in fact, one that was unlikely to be on a male. However, he's also not 18 yet and was going to basic training under some pre-admission program. Under the DoD policy in place as of yesterday, he was still fully a she and to be treated as female.)
The rest will depend on the specifics of the policy. Trump doesn't choose his words carefully and sometimes listening for the gist over several announcements gets you a lot further in actual meaning than parsing each word. He's always had others provide the precision and accuracy that he, well, "frequently lacks" isn't right ... The precision and accuracy that he's never even been in the same room with.
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malaise.
