Is this related to "muintir", by any chance? Or is that a false cognate?
From what I can see, they seem to be regarded as unrelated. Wiktionary  says of the word for "teach": "Possibly from Latin monēre (“to remind, advise, teach”), with phonological influence from mūnire (“to defend, protect”).", while for the "people" word, MacBain  says:
"household, people, Ir. [muinntir], O.Ir. [muinter], [muntar]. This is regarded by Stokes, Zimmer, and Güterbock as an early borrowing from the Lat. [monasterium], monastery; the word [familia] is often applied to monasteries by Irish writers."
Old Ir. múinid might come from Latin, but the tóir suffix does (via Old Ir.) come from Latin -tor
no, but I thought it might be useful and no one had mentioned it yet so I did.
I see it seems pretty close to "monitor", which, somehow, is a way to translate "teacher" to my language.