Gender in the US means male/straight, male/gay, female.straight, female/gay, asexual, bisexual, or pansexual. not just male or female. yes, we borrowed the word from grammar but gender actually means "type" as in genre.
And why not send the woman in if she's volunteered to be in your army? It's her right to do so if she wishes. I wouldn't volunteer, and neither would my sons, but it's out of pacifism, not about sex.