I agree that it does look a little like a house. Unfortunately the term is already associated with residential homes. This is basically an outline of a building. It doesn’t even resemble the larger shrines that require more resources to build.
I would instead suggest using the term “fereter”. A fereter is a portable reliquary. A specialized container designed to safely display religious objects.
It’s clear that, as with many things with OSM, a lot of tagging is built around local conventions and knowledge (thinking of Mercat crosses here). I don’t particularly see a problem with that, and it’s often easier to stick to them than find a satisfactory set of tag values which is more universal.
In this context it’s worth reflecting on how the data might be used: for instance wayside crosses in the UK are nearly all historical monuments wheres in Spain they (and shrines) may be useful for navigation. In many countries they still have religious significance too, much less so in UK.
I confused.
My issue was with calling the glass fronted wooden cabinet a 'house". I agree that it is could be considered “house” shaped wooden box or fereter=house. Anything beyond that is both confusing and a bit of a stretch. It would make it difficult to seperated a stylized fereter and actual home that have been turned into religious shrine when they both use house=wayside_shrine.