While their reluctance is commendable, I'd have thought they'd be used to this sort of thing. It's not all that different from taking out bandits or thieves...
In general principle sure, but there tends to be a major hitch in the mind for people taking someone down for violations of a civic nature instead of those of a religious bent.
It'll be interesting to see which choice they make.
Personally, and I'll own up to this being a wild flaming guess, but my money is on not carrying out the execution and Vegas is giving me 5:1 odds.