This is also Trump's hatred of our African American President Obama. The idea this ban would be reversed is outrageous. The USA military went through a great deal of investigation with the troops. This is not reasonable. The only way a ban could stand now is if it were proven to be adverse to the operations within the military.
The Transgender military members need to bring the DOCUMENTATION forward that was part of lifting the ban in the first place.
As I stated before, the reaction by the Supreme Court is somewhat tainted by the fact this is the president making this request and it is about national security and the military. The fact this is allowed to work through the lower courts before the Supreme Court would consider it, also makes this an election year issue. It could take years for this to work through the courts.