Look, we integrated blacks in an era when many troops came from states that were actively segregated. We desegregated years before the rest of the country. We picked up women and we've almost fully integrated them. There aren't that many jobs where a woman simply cannot serve in anymore. The only ones I can think of off the top of my head is SOCOM jobs, and submarine service. The subs are mostly because it is simply too expensive to rip apart the submarines just to put in the necessary living space for females (Female bathrooms, showers, etc). Submarines are notoriously hard and expensive to modify. All the surface boats are already crewed out with females, a lady freind of mine just got out after serving on a destroyer. She wandered the world in an Arleigh Burke class tin can for four years. Can we integrate gays? Yes. Will there be issues? Yes. Will bad stuff happen? Unfortunately, hell yes. But it is doable. We're the Freakin' US military. There ain't nothing we can't do! And if we can't do it, we'll die trying anyways
I don't know what it's like for the Air Force, but at least for the Navy, this issue is not as simple as many people think. The ability to do your job is not the only part of your job. You also have to live and get along with your coworkers. Unit cohesion is not a requirement of the civilian workplace, but it's critical to the survival of a Navy ship.
Have we successfully integrated blacks into the military? Yes, but that's not the same issue. No one can do something black/white/asian/hispanic upon you. However, they can commit a homosexual act upon you.
Have we successfully integrated women into the military? Yes, but not all areas are equally successful. For example, mixed crew ships often have a high rate of nondeployable women due to pregnancy. I've seen stats of 30-40 percent of the female complement being undeployable shortly before a scheduled deployment. We currently evac females for the same reasons as we do males - illnesses, injuries, etc. - plus pregnancies. This is a major problem. In addition, women tend not to be able to handle many of the firefighting tasks that men can handle due to differences in physical strength. It's nice to think that you can have a dedicated firefighting team of all men to do those tasks, but what happens when your home is in the middle of the ocean and an onboard explosion takes out your team? Think USS Forestal. At that point, you need everyone you can get to be a firefighter.
Does the Navy report mixed crews as a success? Of course it does. Navy captains may get a lot of respect in the movies and TV, but they aren't powerful enough to tell Mr. and Ms. Congresspersons that he and she were wrong in forcing the Navy to implement the program. So it's "Yes, sir, yes, sir, three bags full."
Also, you still need separate facilities for the men and women for a reason. Because mixing naked male and female teens and 20-somethings in the same showers is generally a bad idea. Because the sexual drive is one of the most powerful drives humans have. "Horny as a sailor on shore leave" is not just an expression. It's a reality.
Gays are not more immune to strong sexual drives than straights. To allow gays to serve openly is no different than mixing men and women into the same intimate facilities.
And despite the ban on openly gay service, we still have major problems. When I was in, I was a legal officer (which is not a lawyer but basically a glorified paralegal). I had one case in which I had to administratively separate an individual for homosexual acts. During my interactions with the base JAG for guidance on how to handle the situation, I discovered that the problem of male rape was a significant one. The JAGs shared stories of senior gay officers forcing themselves on junior officers and junior enlisteds. On one ship, the Kearsarge, the problem was bad enough that it was nicknamed the Queerbarge.
"How come I've never heard about this?" I asked.
"Because your Mark-1, Mod-0 sailor wouldn't enlist if he thought he might be raped in his bunk," I was told. "It's bad PR."
None of this is to disparage gays, and if you look at what I wrote above, nothing in it disparages gays. It is to say that gays face the same drives as straights. It is to say that if mixing men and women in things such as shower facilities would cause problems, you'll get similar problems by allowing openly gay people to serve. It is to say that there already is a problem, and to make it worse doesn't make sense.
Can gays do a military task with honor? Yes, and many already have. But doing a military task with honor is not the bigger story. Unit cohesion is.