I think the question is 'what would you SAY to.......'
Well, i wouldn't say anything. I'd ask. The problem here is no one can truly answer because no one has any details. Your side of things make it all sound very minor and petty how she's acting, but what are her reasons? You call things 'trivial issues', but what exactly is that? And obviously these issues aren't trivial to her. Maybe that could be part of the problem. She thinks certain things are important, you think they're 'trivial' and treat them as such.
If you are the 'unbeliever' who is 'departing', i'm assuming you're a non-christian and are divorcing her, by that wording, well, unless you have underage children what is the necessity of maintaining a friendship?
I can only come to two possible conclusions with the almost non-existant details you've given. Either she's a religious minded person who has no real understanding of her faith. Or your actions have given her reason to respond so strongly. So until i know for sure, all i have are questions, not comments.