Does the person making this post believe in the death penalty?
Yes I do.
I don't believe that shedding your blood, though, atones [reconciles you to God] for your sin.
The concept of atonement by Jesus Christ is 100% fine. Atonement as an English word was developed by English reformer William Tyndale in the 1500s. It came from putting together three words - at - one - ment -- being at one/reconciled.
Having your blood shed for murder doesn't reconcile you to anyone.