Thank you all for your comments and replies. You have confirmed my belief that this woman probably should not have a place in the leadership of our Troop. The ASM and his family are some of our closest friends and I wanted a few other opinions before I made a decision. I wanted to make sure my personal feelings weren't clouding my judgement. And, like I said, there is quite a bit more to the story.
I'd like to be clear that I am not questioning that she is hearing from God. That is something the ASM will have to discern for himself and since he is a man of deep Christian faith, I do