>>Do federal judges have any standing on military matters?<<
They should not.
I am surprised the Trump Administration has not taken this to SCOTUS as yet another example of Judiciary interfering with the Constitutional powers granted to POTUS.
There is more here than a trans ban (I assume there will be so few that actually make it past basic to be almost meaningless). This is a separation of powers issue and MIGHT be the case Thomas wants to finally slap down the lower courts for continuing to think the Judiciary is the only branch of the US Government.
There are trannies in the military now, mostly “under medical care.” They are the troops who decide after they are in to change the little things.