"Holy matrimony" is the business of the church, and if they have any complaint it should be that a "marriage license" is an intrusion into something that is not the business of civil authority.
The "marriage license" exists, or should exist, only to make visible to the community at large that a civil contract exists permitting either party to act on their joint behalf or to execute powers of attorney on behalf of each other in matters of civil law.
Demanding that the civil certification that a contract exists must prescribe what kind of sex the parties to the civil contact are permitted - or required - to have, the bigots are FORCING an even more intrusive civil interference with what they call "holy ritual and covenants."
The assumption that SEX - of any kind - is the only thing that marriage is made for reflects a pretty low opinion of one's own faith and rituals.