Religious communities / peoples in the US are actually being frightened that this scenario will play out. And it's no good to say that they are just scared of some weird slipping rope argumentation that is stupid and will bear no fruit, when all these changes that seemed impossible just a few years ago just turned out true.
The future is fought and built for every single day, and this achievement only makes that point even truer than ever before. I can indeed see how some fringes will eventually try to sue churches who do not marry gays for discrimination. It's not as if people were not up in arms a month ago about some bakers who refused to bake a gay wedding cake, and sued them for that exact same thing IIRC (or at least that was the argument). I do not believe most gays will even think of trying to do that, because of the simple fact that it is an assholeish thing to do. If a church has a definition of marriage that is heterossexual only, why would you force a priest doing something he really believes to be a farce?
Nevertheless, I can totally see a case or two propping up, due to very specific circumstances of some curious backstory or something to that effect. It's bound to happen. And the Christians are totally expecting it to happen and they are also expecting all sorts of media campaigns against their "bigotry" when it happens. It will be ugly to watch. Reasonable people won't do this, of course, but these campaigns are not leveled by reasonable people. And if some random judge happens to rule against one church or two, mayhem will occur. "Culture Wars" will rise to a whole new meaning.
It's a scenario that I for one have no desire to watch being played out, so I really hope reasonableness and common sense may prevail in the future, and all incidents of this sort may defuse and be treated eloquently and sensibly without stepping into these christian's throats.