I wanted to make a distinction here, maybe most will not care but still.
Batman in BvS does not commit pre-meditated murder. He doesnt go out of his way to go murder someone to take them out(until Superman, and even then he didnt go through with it). He had guns in his Batmobile. He could have blown everyone away during the chase. He could have just shot people with his gun in the warehouse and take everyone out(like he did in the knigtmare scene). He didnt. He engaged in hand to hand combat and relied on his gadgets. He only shot, when he was being shot at and had no option. Same when he was in the batwing, he even gave warning shots. Make no mistake, if he didnt fire back, he would have been dead/blown up himself. Even in the warehouse, he could have just killed the russian with a headshot. He didnt. Batman as shown in BvS, kills. But he kills in self defence, or rather he is reckless enough to not care if someone dies in battle with him. He does not outright murder someone in cold blood, punisher style. The movie criticises his reckless and cruel behaviour, and Batman in the end promises to do better, and we see him change by not branding Luthor.
Does that make a difference? Maybe, maybe not. If you purely look at it as a black and white "KILL/NO KILL" way, then yeah he is a killer. But in real life, there are nuances to the killing thing, where sometimes its justified. Cops are allowed to kill...in self defence. That doesnt mean they are no worse than the people they are up against, nor that ever mean that now that they have crossed a line, they will just keep murdering people left and right. Its not good logic, nobody thinks that way. I think Nolan's Batman also killed or rather had reckless kills(the ninjas, Dent etc). Burton's Batman was a straight up murderer. So I think there's a sense of moral justification there.
I think post Superman's death Batman or pre BvS Batman...had a code. That code was save as many lives as possible, without killing. And not being a cruel mf obviously, no branding and ****. Snyder is going to be asked about Batman's code pre Robin's death in the IGN panel(submitted question), it would be interesting to see his response. Now what happens in the knightmare timeline? Batman murders. Yes. Do I think that's okay? No. Do I think that's justified? No. Do I accept it in a story where everything has gone wrong(Superman evil, most JLers dead, earth destroyed)...yes.
As for the argument that he had a redemption, how can he go rogue again? Well I would argue that not only is it realistic, that people fall again after a redemption(you can liken this to a relapse) but we have seen similar arcs in acclaimed shows/movies. Jesse Pinkman in Breaking Bad for example.
Here's the thing. Snyder deliberately puts Batman in situations where he would HAVE to kill to survive. Where he would have no other choice but to kill. In situations where if he doesnt break his code...people will die. Now what would Batman do? Not kill and let people die? Or break his own code, and save people? There's no other option, because they as a writer wont give him an easy way out. As Snyder put it, the "Kobayashi Maru". That's disturbing to see, because we are so used to Batman always finding a way out. But I think its interesting. Its also what I think Miller did with the child rescue thing in TDKR, but he was smart, he left it ambiguous. Why do this? Well, its very simple to write a story where he says "I dont kill" and never put him in a situation where he needs to. Its extremely simple. I think its far more interesting to put him in a difficult spot, and see what effect that has on his psyche. It could/should be explored way more than it was in BvS(mostly wasnt because that movie was a ensemble, and not really a pure Batman movie and had so much else going on). I think a story like Redhood where Batman doesnt kill and that results in a huge calamity could be a very interesting story to tell. Its deconstructive, so I totally understand if its not your cup of tea.
