I don't understand this stupid obsession with group showering.
It's not an obsession. It's just a cost effective mechanism employed in certain settings. By the way never join the military if this ruffles your feathers. The stories my friends told me from boot camp would give you a heart attack.
Military ≠ High School gym class
High school gym class is for most everyone. The military is not.
Doors aren't expensive, and even if you want to keep the cheaper group showers than maybe have one "special" shower to make sure that transgender students don't have to go into the shower of the gender they don't identify as. It would be exclusionist but useful to preempt unwanted drama and angry debate.