@revelette2,
It may make a difference legally... at least that is what her lawyers are arguing.
The state of affairs as of today is that she is neither issuing the licenses herself or giving any permission for the licenses to be issued. She is simply not preventing the licenses from being issued.
Employment law provides that "reasonable accomodations" should be made for people's personal religious beliefs. It will be interesting to see how the current policy will do in court.
But, In this way her personal religious beliefs do make a difference legally.