For a long time it was part of Captain America's character that he NEVER killed anyone (and, believe it or not, for a LONG time this INCLUDED World War 2)! There's even an issue in the Mark Gruenwald run that deals with this, when Cap finally has to take a life (an Ultimatum agent). Later, future writers, [like Ed Brubaker, writer of Captain America Volume 5], chucked that right out the window (or rather swept it under the rug) and pretended that those issues happened ANOTHER WAY [...] because in their minds there was no way a soldier like Cap went through all of WW2 without killing some Nazis.
And most readers are fine with this, accept it, and keep reading.
Same goes for issues where Flash Thompson and the Punisher fought in Viet Nam. Same goes for a lot of the old-fashioned sexist views of many of the characters. Everything gets a gloss and the comics you read in your youth didn't happen EXACTLY that way... but they happened.
-Amazing Spider-Man writer Dan Slott
I'm currently reading Captain America volume 4, and it appears that writer Chuck Austen not only stuck by the "Captain America didn't kill, even during the war" thing, he wrote a story about it, that was also intended to give a more "realistic" explanation for why Cap ended up frozen in ice:
Captain America volume 4, issue 16 was Chuck Austen's final issue as writer. I haven't read the rest of volume 4 yet, but I'm guessing the writers that follow ignore this whole thing or eliminate it. I sure hope so.