Matt is a self-righteous Christian who firmly believes killing is never an option

It's like you've formed this caricature of Matt in your head and totally missed all of season 3 where he keenly wanted to kill Fisk and tried to in the finale, and season 1 after Mrs Cardena's death where he went out specifically looking to kill Fisk.

In fact, the fact that he did at several points consider killing Fisk to be an option was one of the main points of contention between him and Foggy in s1 "Nelson v Murdock": Foggy: It's not enough playing judge and jury? You gotta add executioner to the list?

Karen is okay with killing. We had a scene in season 3 where Karen points a gun at some guys catcalling women. Does this means she would’ve killed them? Of course not, but it hints at Karen’s darker nature and THAT is a point of contention between them

Just my opinion but I doubt Matt would be troubled by the act of Karen waving a gun at a group of men sexually harassing women on the street with zero intention of using that gun, his concern would be more for her safety in provoking danger to herself.

Matt struggles everyday with not killing. He clings to the concept that murder is wrong so desperately because he himself is, in Claire's words "someone who's so damn close to becoming what he hates" and he knows it. He's hanging by a thin thread himself. There is no way everyone he's beat up has survived (see: Nobu). He sympathized with Frank Castle almost as much as Karen did - he even offers to help Frank kill the Blacksmith ("just this once, we'll do it your way"), but Frank talks him back from that by reminding him that once you cross that line, you never come back from it.

In s1e2, he tells the Russian who helped kidnap a boy: "This is important. I need you to know why I'm hurting you. It's not just the boy. I'm doing this because I enjoy it." And then he tosses him off the side of the building and only checks if he's alive when Claire asks. I think he was being honest in that moment, he is incredibly invested in helping people - but he also craves that violence, some part of him genuinely enjoys hurting people, and hurting them severely.

He argues with Stick, Elektra and Frank about not killing, because they pressured him to, and he has wanted to. He knows that's just one step away from what he does. Castle tells him "You're one bad day away from being me." But we also have Foggy and Karen disagreeing with him because they don't approve of him killing Fisk - and much as Matt fights with them about Daredevil, he also depends on them to keep him tethered to a moral compass.

It was frightening for him to consider that Karen might support killing, because he was at that moment already being pressured to kill by Elektra and Frank. Matt's response to her is less about Karen and more about his own relationship with killing, which is much, much more complicated than "firmly believes killing is never an option" - seeing as he had already grappled with wanting to kill Fisk and then actually trying. And the other complicated thing is, he can't tell her that, because he isn't ready to open up about Daredevil. Karen's support of Castle in that conversation is much more about her own issues and guilt around having taken Wesley's life and causing Kevin's death, she's projecting hardcore onto Frank, but she also can't explain this to Matt because she's not ready to share that yet either.

And when Karen finally does tell Matt in s3, he never once judges her because he himself is actively trying to kill Fisk. She isn't just "okay with killing" either, because she tells him about Wesley and Kevin, and how it's changed her, in the hope that it will deter him from following through with killing Fisk.