...you are licensed through the state.
This is not the case, no one is formally 'licensed' to perform weddings. Ordained ministers and other religious leaders are allowed to sign the marriage certificate and have it be valid. If asked, they have to show that they are indeed a minister, that's all. Here in Florida, Notary Publics may also solemnize the marriage by signing as can clerk of courts and Judges. Not one of these is licensed by the state but some are state employees. Only state employees could not refuse to marry someone due to them being gay.
From a clerk of court website in Florida
Who may perform marriage ceremonies?
A regularly ordained minister or other ordained clergy;
Elders in communion with some church;
All judicial officers (judges) of the State of Florida;
Clerks of Circuit Court and their deputies of the State of Florida; and
Notaries Public of the State of Florida.
In addition, the law provides that marriages may be performed among "Quakers" or "Friends," in the manner and form used or practiced in their societies.
Note: Boat Captains are not authorized to perform marriage ceremonies in the State of Florida unless they are otherwise qualified as provided above. Marriage ceremonies must take place within Florida’s boundaries (within 3 geographical miles of the coastline).
Who is a "regularly ordained minister"?
He/she is a minister who has been recognized in the manner required by the regulations of the respective denomination to perform marriage ceremonies.