In the eyes of roughly half the country, it's plainly injust to allow anybody to murder what they believe to clearly be a human being just because the other half believes they're subhuman.
It's the government's job to punish injustice, even if the actors don't believe they're being unjust. Very few people in prison will say they did anything wrong. In their eyes, their crime was justified. Everybody thinks they're doing the right thing. Like it or not, it's the government's job to determine if that's true or not in many cases.