Denmark has a state church. When your “church” is a tax funded government institution, and most taxpayers want you to do same sex weddings, you need to do what the boss tells you. Will not happened here as long as churches stay independent of the government.
A judge could choose to apply "antidiscrimination" law to churches any day, just as they have with private businesses. It hasn't happened yet, but I think it's only a matter of time, since the official line from the Supreme Court is that only evil, ignorant, bigoted people oppose "marriage equality."