Not allowing gay military personnel to shower with straight military peronnel would be "discrimination." That's the position of Rep. Barney Frank (D-MA), an openly gay member of Congress who is a proponent of banishing the military's "Don't Ask, Don't Tell" policy.
Frank told CNSNews.com that the idea that people might be concerned over gays and straights showering together, and the possible disruption it could case, is a "silly issue":
“To accept the principle that homosexuals can’t shower with other people is a degree of discrimination that goes far beyond this. We don’t get ourselves dry cleaned. We tend to take showers when we go to the gym; when we play sports,” Frank said.