I believe that the military is checking for HIV status as part of a routine medical screening before induction and rejecting the infected, but that might be deemed "discrimination" in a future gay friendly military.
I don't think that bleeding from wounds will cause a lot of HIV infections; but the perception of risk would certainly inhibit contact with men of uncertain HIV status which might inhibit combat effectiveness.
Another concern is with emergency blood transfusions which are done in combat situation where FDA approved blood products are not available or whole blood is preferred. See Emergancy Blood Transfusions
Why not, if infected blood splatters or spills on other people with open wounds, cuts, abrasions etc. That's why EMT and other health workers are so dang careful! They don't want to get AIDS or other blood borne illnesses.
“I don’t think that bleeding from wounds will cause a lot of HIV infections;”
In combat, the injured don’t just bleed; they often spray or explode in blood and other bodily fluids. This presents risk for anyone in the spray radius. You might want to read the book “American Knight,” a biography of the late Col. John Ripley, USMC (Ret), who suffered two liver transplants, quite possibly the result of constantly being rained on with the blood of wounded warriors in his proximity. And they were non-HIV injured, so you can probably extrapolate the inference.
Besides, if simple bleeding is no risk, why are boxing officials, trainers and corner men required to wear protective clothing? Or detectives at crime scenes? I could go on, but you get the point.