This is a genuine question. As a Christian, I am often asked by atheists why I don't think adulterers should get the death penalty when Leviticus 20:10 clearly says that they should. My response to them is very simple: Because I believe that John 8:7, a verse in the New Testament, supersedes Leviticus 20:10.
Rabbinic Jews, likewise, seem to have derived from the Talmud several restrictions on capital punishment making it impossible to carry out (i.e. requiring 23 judges, 2 witnesses, etc.)
Now this has recently got me thinking: Karaite Jews don't believe in the New Testament or the Talmud, right? So according to Karaite Jews, every single law in the Old Testament remains binding, right?
Now suppose Israel became a Karaite Jewish theocracy governed by Biblical law. Then would Karaite Jews go back to stoning adulterers?