The correct recourse for these sheriffs is to file suit. In the mean time, what the people voted upon is law, whether the sheriffs personally agree or not, and their job is to uphold it.
Well, the problem here is that there are varying opinions on what exactly is “constitutional.” There is a field of thought, even among this thread, that there can literally be NO infringement of the right to bear, even among those convicted of crimes. “Shall not be infringed.” Others side with Scalia (aka-the courts) when they said that the right can be taken away with due process. “Shall not be infringed.”
There are varying degrees of which court findings are acceptable and which are not.
Which is why we have the judiciary in the first place.