The correct response to a public employee who is "uncomfortable" doing their job is to fire them and hire someone who will. But this being Florida and Jesus and all, that won't happen:
Generally, when a couple heads to their local courthouse or county clerk’s office, they can both receive a marriage license and have their marriage officiated. That is no longer true in 14 Florida counties that have changed their policies anticipating the arrival of marriage equality this week.
Clerks in those counties have offered various justifications to the Tampa Bay Times for ending their courthouse wedding services, including cramped offices, staff limitations, and shrinking budgets. Others admitted that same-sex marriage was a contributing factor.
Pasco County Clerk of Court Paula O’Neil said that most of her staff were “uncomfortable” officiating same-sex weddings, and ending the practice was the only way to avoid discriminating or transferring them all to different departments. Okaloosa County Clerk J.D. Peacock II told his staff in a memo, “I do not want to have members of our team put in a situation which presents a conflict between their personal religious beliefs and the implementation of a contentious societal philosophy change.”