Currently, my fiance and I are not members of a church, however, we would like a religious ceremony with a minister officiating. Is it appropiate to call churches and ask Ministers to perform a wedding ceremony when you are not a church member?
Yes, it is most appropriate! Churches are used to this kind of questioning. Every church and denomination has different rules. Some churches require that you become a member. Others do not. Some will allow you to just rent the church. Some will want you to convert to their denomination. Sometimes it is a religious issue, and very honestly, sometimes it is a question as to whether the church needs the money. Unitarian Universalists will certainly allow you to marry in their churches. Try local churches that appeal to you in your area. Try the yellow pages. Google.
Do the research, and the right church and the right minister will manifest itself... You will know when it is right. You will feel a connection.