Why can't people with an STD join the military?

Two reasons. The primary one is they don't want you going to a unit and giving your STD to people. But just as important is the military still subscribes to old Victorian standards of morality, and sex is a serious taboo there - the military still has its sodomy law, which allows them to put you in prison for 20 years for non-missionary-position sex. They don't enforce the stupid thing unless you did something to go along with it - if you get nailed for rape they'll usually throw a sodomy charge in there too - but they are the only ones who are allowed to prosecute for sodomy.