How do I ask?

I received a package from a distant cousin a couple of weeks ago. It contained some genealogical information and was much bigger than I expected. So it is taking some time to review. But I wanted to share some anxiety I felt. The cousin who sent the info is descended through a branch of the family that did not follow Brigham Young to Utah. Her ancestors followed Lyman Wight and eventually joined the Reorganized church (now the Community of Christ). I know she knows where my side of the family went, and I see data obviously provided by LDS researchers in the past. One was my grandfather which is kind of cool. But I am hesitant to ask the question of her religious affiliation. It's silly, I know, but there it is.
Part of my hesitation is that ...
1) Religion is almost a taboo subject to discuss, at least in the USA, and although we are cousins, she is basically a stranger.
2) I don't know how to ask. "Are you Mormon?" doesn't get specific enough to remove the abiguity. She may be Mormon but not share my denomination.
3) Her answer really should be irrelevant. It should not change our working relationship. So why even ask?

And for those of you who are both curious and nosy, I did eventually ask. She does not belong to the CoC. She joined the Mormon church as an adult not originally knowing her family's ties to Mormon history.