There is no reason why transgender people can't be given a place in the army, so that comparison is dumb. Colourblind people maybe can't fly planes because they can't see the bright lights on aerial towers or something. The only arguments people make against transgender people in the army are fiscal ones, like "Wehhh, it'll cost too much money." Or "Wehhh, we'll have to make some slight changes in how we do things."

Arguments about the mental health/stability of transgender people I don't consider legitimate, BTW, for the reason I gave in another post above concerning homosexuals.