Can they turn a couple down for a ceremony based on skin color? No? Well then, they can't turn down the deviants, either. Both are now a "civil right".
If you're talking about government officials (e.g., county clerks, justices of the peace), you're probably right. If you're talking about churches, you're wrong-- no one in the US has ever successfully sued a Catholic church for not performing a wedding where one of the spouses is divorced, and no one has ever sued an Orthodox Rabbi for not performing an interfaith wedding.