I did a bit more googling on the subject. As best I can tell from some superficial research, in the British and American militaries, "transgender" only refers to those people who have started, or completed, a process to surgically alter their anatomy to resemble the opposite sex. A male soldier who shows up and declares that he self identifies as a woman isn't a transgender under the regulations. He's a man, who perhaps ought to seek a doctor's assistance and consider some sort of diagnosis and treatment. As best I can tell, in the American military, the identification of someone as transgender begins when there is a doctor's diagnosis, and a treatment plan that ends in a transition to the opposite sex.
I also learned that, tweet or no tweet, transgenders cannot join the US military. An Obama administration directive ordered that the armed services start admitting transgenders as of July 1, 2017, but Mattis asked for an extension delaying that implementation. Transgenders who "came out" after entry into the military are currently allowed to stay in. If that tweet is translated into a policy, it would seem they will not be in the future.
I can't believe we elected an idiot who would put out a tweet like that.