I’m having trouble understanding or grasping an idea

Okay. So. I just finished watching the Ted Bundy tapes and it brought into light another issue I’ve been struggling with lately as a follower of Christ.

It’s the death penalty. In the Old Testament, the law was eye for eye, life for life etc. But after Jesus died on the cross, that changed and Jesus became the way. He’s the reason we have a chance even though we are sinners and don’t deserve it.

Obviously, murder is wrong and death penalty is murder. But from a Christian perspective, can someone claim to be a follower of Christ and support death penalty?

The ONLY sin ever mentioned in the bible as unforgivable is blasphemy against the Holy Spirit. Now, in God’s eyes sin is sin. There’s no one that’s lesser than another, even though to us we think of them as extreme differences between sins (I.e. lying vs murder), but to God he doesn’t see someone who lies as a person who is automatically better than a murderer. In gods eyes we both need redemption and at the end are both sinners. God can forgive someone who murdered another or someone who raped someone or whatever.

So with that, how can we justify death penalty from a Christian perspective? I mean, at the end of the day its murder no matter how you look at it. We shouldn’t get to play God because of something they did. They’re going to have to face him someday anyway and it’s worse than any earthly punishment they could go through if they don’t accept Jesus.

I get that, I get that following the bible, living a godly life and following Jesus, death penalty is wrong, but I can’t help myself from thinking some people just deserve death. So really what I’m asking I guess is, how can I change my thoughts from someone deserving death to a more godly thought?