>Would it be okay for a government worker who was a Quaker to refuse to issue gun licenses because it's against her religion?

It certainly would be OK, if that Quaker is willing to go to jail for that act.
In fact, if I were in that position and someone came in with an AK47 to license I might be tempted to do just that.
I probably wouldn't though, because I've come to like my creature comforts.

This is passive civil disobedience, as opposed to crazy people who bomb abortion clinics.

The only victim in the case is Kim Davis, who has shown herself willing to go to jail for her beliefs.
As I said, I disagree with her, but I admire her courage.