From the headline, I assumed that it involved a Christian minister who refused to conduct a religious service. If that were actually the case, it would be wrong.
But the case involves a government employee who refused to serve the public, citing personal beliefs. Of course, everyone is entitled to their personal beliefs, but if those beliefs interfere with doing the work you are asked to do then the sensible, and honorable, thing to do is to resign. A Muslim butcher who was asked to handle pork would likely quit, if s/he took their faith seriously. I don't see how this situation is any different.