I've heard a lot of controversy over whether or not pastors who deny same sex couples should be fined, jailed, etc. If the pastor is licensed by the state don't they then have to be religiously unbiased like any government employee or establishment?
The connection between priests and marriage is via laws regulating the solemnization of marriage. Washington's RCW 26.04.050 is typical:
...Justices of the supreme court, judges of the court of appeals, judges of the superior courts, supreme court commissioners, court of appeals commissioners, superior court commissioners, any regularly licensed or ordained minister or any priest, imam, rabbi, or similar official of any religious organization, and judges of courts of limited jurisdiction as defined in RCW 3.02.010
Not ship captains, notice. Solemnization is not required. RCW 26.04.010(4) says
No regularly licensed or ordained minister or any priest, imam, rabbi, or similar official of any religious organization is required to solemnize or recognize any marriage. A regularly licensed or ordained minister or priest, imam, rabbi, or similar official of any religious organization shall be immune from any civil claim or cause of action based on a refusal to solemnize or recognize any marriage under this section.
There is no similar waiver for non-religious officiants. The First Amendment is theoretically what has limited governments ability to require priests to violate their religious beliefs; but I would not be surprised if that changes in the near future. In which case, permissive laws like the Washington law could be trumped by federal anti-discrimination law.