They can do the wedding ceremony, it just isn’t legally binding. What’s the problem? Religions which recognize polygamy perform their ceremonies, they just aren’t legally binding.
This is bogus, because nobody is preventing them from performing a homosexual ceremony, if their religion allows for that.
Bingo!
The basis for the lawsuit is a North Carolina statute which makes it a crime for a clergy member to perform a wedding ceremony unless the couple has a state-issued marriage license.
The correct resolution of the lawsuit would be a ruling that it is unconstitutional to apply that statute to clergy who perform a religious wedding ceremony so long as no one is claiming that the marriage is legal. The correct resolution is not to say that the State must recognize as legal any marriage that any clergyman wants to perform.