Should the State enforce laws against adultery? - Yes.
Will the State do so? - No, not until God grants repentance and faith.
And let me go ahead and "drop the other shoe". To what extend should the State prosecute those found guilty of adultery? - To the fullest extent of Biblical Law. Yes, that means the death penalty, but only in so far as the State is Biblically oriented and has the proper laws enacted (i.e. laws that align with "The Law").
*Running for cover now*
[
Seriously though, I have to go out on some sales calls. Will be back later today to take my lumps. 
]