What rights should people have when the duties of their job go against their religion (see details)?

Town clerks are resigning left and right in New York state right now, as gay marriage is newly legal here and once the law goes into effect, part of their job will be signing marriage licenses for gay couples.

What do you think? Are these people bigots? Police officers don’t get to pick and choose which laws to enforce based on their beliefs, so should these town clerks just suck it up and sign the licenses? Or should these town clerks have special rights so that they’re not forced to do anything they believe goes against their religion?