The use of denomination=mormon dates back to when that was the official name (church website was mormon.org). Even since, mormon has been by far the most popular choice for new additions, and thus the one recognized by data consumers.

For the temple, building=temple is enough to tag it as not a church (even if a lot of data consumers might still interpret it as such). The value of religion still needs to be fixed, though.

Apologies for missing that you used the building=house house=detached tagging scheme. That is only used frequently in Ireland. Basically every other country uses building=detached far more frequently.