Don't worry about convincing her that she's dishonorable. You don't need to do that. Your lady-friend is part of a faith-group that practices cult-like mind control. They don't want her with you. She has decided to accept the control of this group. If you are not interested in having this group and its minister all up in your business, then you may have to just accept that this relationship cannot be maintained at this time.

You certainly have the legal right to vent in a letter to her. It's not always good to do something, even though you have a right to. She has a right to be loyal to this group. She has a right to decide that the religious difference between you is too great for her. Do the standup thing, and exit gracefully.

Of course this is frustrating. You tried to meet her half-way, but it does not sound like you would be happy in this church group. I know I wouldn't be. If she was raised by parents who were part of this religion, then she may be there to stay. If this is a group she joined as an adult, then she may eventually become disillusioned with it and drop out. Maybe, step back, and see what happens. You and her don't need to become defensive toward each other. You both have the right to your preferences. Try to part without rancor. You'll be glad of that down the line.