I'd say it goes back a little further than christians and oblates. Surely, most temples are kept well clean so that a mouse wouldn't find much to eat. The church tending to the poor can be associated as well as some kinds of church striving for purity.

Puritan, poor, pure, you get the gist. Actually, these are not said to be related, with peh₂w- and pewh₂- reconstructed, respectively. But in my humble opinion, "humble" could semanticly connectboth. peh₂w-, whence poor* and few, is also the root to pupil and puberty, via Latin pūpa/pūpus. On that note, words for orphan have been surprisingly productive, orphan supposedly giving German "Arbeit" - work, its origin unsure but perhaps connected to orpheus. Maybe orphans nominally under the care of the "father" are the mice in question. Mouse is a humbling diminutive, at least in German. In the pied piper, children are compared to mice. Boy can mean male servant (it's root is not compare to these here, though, might still be in an older layer of the languages' roots). Spanish puta is still unexplained, but Portuguese has puto (boy), Italian puttus (child) - said to be cognate with, no not pupa, but purus. Spanish and Portuguese also have moço, moço (boy, girl) of "unknown origin". But they do use rat related words for mouse instead, while muro is archaic. Baltic languages have instead pele (mouse), from pel- (grey, alternatively pelh), whence also pale. Surely, grey mouse is a synonym for plain, which is one of the glosses found for poor. Plain again is from pleh₂-, which derives several words for thin, flat, further tame* and perhaps also plague. Plage, Blage is a dysphemism for children in German. A page is a young servant in French and a page of paper is plain and flat. mew- also derives a sense of small, but whether that pertains to mouse or not is debatable. There's also mey which could be confused, meaning e.g. to change. Another spanish word for boy is muchacho, from mocho (mutilated, incomplete; hornless; having a hypocritical and ostentatious faith; cut short; bald headed), of uncertain origin). Then compare patch, patchy hair to page or Russian plóskij (flat, plain, level, tame, trivial). I mean, chico (boy) probably relates as much to chick as mouse to maid. Mouse rather rhymes with house (the house mouse), therefore compare house, husband and husbandry. I have no idea where this might lead, possibly astray, though.