It's already starting. Just look at the U.K. if you want to see where we'll be in a short time.
Activists are already starting to demand this since ministers are made agents of the state for purposes of finalizing the marriage ceremony, they must be made obligated to the requirements of the state as far as marriage recognition. Mark my words, within two years, churches will be threatened with performing fake same-sex "marriages" or the pastor will be prevented from performing any marriages at all. That, or the church will lose it's tax exempt status - possibly both.
The New York "religious protection" amendments to the marriage law are not severable (how convenient for the sodomites,) so if one is found "unconstitutional" by an activist judge they all go down the drain.
Will Islamic mosques and Moslem clerks be required to comply as well I wonder?