If they want to maintain tax exempt status, yes. Watch. It’s next. This ruling decimated any chance of religious freedom in America. Your religious freedoms are GONE, according to FedGov. You might want to take a hardline stance today, or sit down and accept your chains, peasant.
I’ll hedge a bit and say that you can never lose your religious freedom. You can be tortured or executed, but you can put up a hell of a fight before it comes to that. Jesus talked about shepherds defending their flocks. American churches are not led by shepherds, but rather, sheep leading the sheep. As long as that doesn’t change, then the hedge is that, yes, you can lose your religious freedom. Or one can be like Jesus, and stand his ground regardless of what the church sheep think or how they behave.
I believe that organized religion/churches have been consorting with the devil for too long. They are about to get burned. My libertarian leanings say marriage should be entirely a religious affair and that the government should have nothing to do with it in any manner or derivative, but society has long disagreed with that and coupled the two together. Live by the sword, die by the sword. Marriage is fast becoming a dime a dozen institution and its going to get a lot worse before long. I think churches need to decouple their affairs and beliefs from Caesar. Not exactly sure how best to do that, but there has to be a way. Giving up tax exempt status is one way. NOT recognizing any marriage outside of their own church is another. They need to make every belief a core tenant of their religion, trumpet them, and wrap themselves in the 1st amendment's freedom of speech (and belief). My two cents.