I'm more interested in how the public feels about punishment for the sake of inflicting suffering on the criminal/accused than actual government policies, though presumably the two would be closely related.
This all started when the person of Christ was co-opted to become the (conveniently deceased) figurehead to a bunch of institutions, his name on the one hand and his followers adopting his name but not really paying overly much attention to the principles (assuming history as recounted is accurate, likely it is not) is the root cause of that.
Imagine that your 'personal brand' of good intentions is stolen from you and re-purposed as a fig-leaf to cover anything from warrior popes to insane riches and abortion clinic attackers. In light of your comment of course 'no true Christian' would ever do anything like that.
I suspect Christ would not be pleased about a large chunk of those that lay claim to being Christian.
The premise of that story, exploring the difference between followers and believers can be mapped directly to... well, quite a lot of religions, I'd think.
So the difference is that a True Christian would, e.g., explicitly focus on pursuing the Golden Rule[1], whereas a No True Christian would conveniently ignore or bend it at their convenience.
[1] "Do unto others as you would have them do unto you". Famously spoken by Jesus, quoting Hillel.