A few quick points - by going into the substantice details regarding the how, you are going into way more detail than what the president gave in his statement. This is similar to the "Muslim Ban" Trump kept repeating that it was a Muslim ban, but in reality it was increased scrutiny from a handful of countries. But on the same day as the AG argues the finer points on this, Trump doubles down and declares that it is in fact a Muslim ban.
Obviously there are going to be ways to get around this for a particularly ardent individual but by his statement, Trump is prohibiting a class of people from an entire sector of government. to me, it is irrelevant that this is likely to be walked back in its application, the President of the United States issued a degree that Trans people are no longer permitted to serve in the military.
Even taking the polarizing aspects of this out of the equation, the fact clearly remains that a group who Trump Championed and used his support of as an attack on his opponent, the LGBT community, he has now betrayed that community with this action. There is no way around that.
To my point about a tooth, first, certainly didn't mean that in a military context, I meant that from an insurance perspective and how they differentiate between necessary and elective surgery. I can tell you from personal experience that correcting a dead miscolored tooth is not covered by dental insurance because it is deemed as elective. The reason I included this was to innoculate my characterization of a gender surgery as elective by grounding it in an objective reality of insurance policy, to demonstrate how high that bar can be.