Churches can just get out of the business of handling the paperwork for the state regarding marriage. Folks can get ‘married’ at the town hall, or by some agent of the state, anywhere they wish. If they wish, they can have a religious ceremony in the faith tradition of their choice, at any time. If that ceremony has nothing to do with the State, how can the State demand anything of them, with regard to who is, or is not, allowed to have their union ‘blessed’ in any Church?
Under the present interpretation of civil rights laws, the state (usually a State, specifically, but sometimes a city, county, or other governmental unit) has the authority to coerce private organization to provide products and services, whether they wish to or not.
If they can compel (or fine, or withdraw licensing) a bakery, florist, photographer, or event venue to serve a homosexual couple, do you think the next step won't be applying coercion to a religious organization which doesn't want to perform a ceremony?
Note that these things are happening already, even where homosexual "marriage" is not recognized by law.