How should I map a church building which is now a private house?

It's still totally OK to tag is as building=church. According to the wiki, the building tag describes the "building typology", i.e. how the building is constructed. It does not say anything about its current use (if any); that is addressed by amenity=place_of_worship.

Note that while the external appearance/structure of a building and its use often go hand in hand, that is not necessarily the case. For example, there are many places of worship that look like regular houses, or convention halls (e.g. small prayer houses, or big modern churches), and conversely there are buildings that look like a church, but are used differently (as in the case you describe). Thus the separation between building= and amenity=.

If it is built as a church, tag it as building=church, if it is not used as one, do not add amenity=* or any other religious information. I do not think that this is common enough to have a special rendering style for church buildings used as private houses...
I do not want to change it in map just to see how it looks, but I suppose it would be rendered grey as a church, but without any cross. If the same building has more numbers, you can split it or use address nodes instead of putting addresses directly on the building. The later being probably smarter for divided church.

I'd treat it as a case of "what does it look like?" That is, if it still CLEARLY looks like a church, by all mean put building=church, possibly with disused:amenity to prevent people from adding that tag (unless it's residential, there are plenty of tags that can be used to mark its current use). If youcan't tell it was once a church unless you know it, tag it as a house/flats/school whatever, and if you feel like it, add appropriate old_name and disused: tags.