Actually, I manually changed the temple from "Church" to "Place of Worship" by selecting it.  It did not do that automatically.  It was an intentional change on my part.

You mentioned checking the wiki -- which I did -- and found this page which is the topic we are discussing and, I believe, making the same point.  https://wiki.openstreetmap.org/wiki/Tag:denomination%3Dmormon

I wondered if there was some kind of typo because I wasn't seeing the "latt" you mentioned.  But I looked deeper and found that.  It was my error by entry in the wrong field; I've corrected that.

I see what you are saying about the building=detached vs house=detached.  I had just selected House and then added the detached tag.  But I saw the difference and believe I have now made the changes as I think they should be per your notes.  Feel free to check and confirm.