I've been to at least two weddings at The Hitching Post. I have in-laws in Coeur d'Alene and I'm very familiar with the place.
The Hitching Post is a for profit business. The only things you need to get married there are a valid marriage license and the fee. They do not ask any questions about your religious beliefs. You do not have to be a member of any church. There is no membership at The Hitching Post, any more than you have to a member of something to get married by an Elvis impersonator in Las Vegas. I believe they claim to have married 35,000 couples there. I had no idea the owners of the place had any religious affliation until this story broke. If they want to be pastors, they should start a church. If they want to act as officers of the state by signing marriage licenses (a legal document) they have to follow the law.