Seems to me a very simple solution: Churches just bestow the sacrament of MATRIMONY upon those who qualify under church precepts for such a sacrament, or rite in churches that do not consider MATRIMONY a sacrament. Whether the state recognizes such rites as marriages is a matter between the church and that state for the state to decide.
Recalling the rending advice about Caesar and God, the Churches are NOT marrying anyone under the civil law. (In a similar fashion, the State cannot demand that churches allow women to be priests.) It has nothing to do with tax exempt status IMO and I see no potential for any church losing it as long as they do not REQUIRE their rite to be acknowleged by the state. If a state considers the church rite to be a legal marriage, as they do in common law situations with no church or civil ceremony, so be it.
The end result would be the exact opposite of "silencing" them, wouldn't it?