Depends on the locale. In the Freljord that shit's probably not 100% common but a major thing that affects daily life. In northern Shurima meeting non-humans is likely not all that common, but in the south there's Voidborn to deal with on occassion. If Alistar's anything to go by meeting Minotaurs on the Noxian plains probably isn't too unreasonable of a thing to occur.
But then you get to places like Demacia, where meeting non humans is probably super rare, Piltover and Zaun, where despite the oddities, there's no guarantees of actually seeing anything that isn't human (And given the weird state of yordle lore they're probably not anywhere near this either, at least not to a large degree). Bilgewater probably doesn't see many non-humans going around either.
Ionia is weird so I have no clue. On the one hand they have a mostly human roster. On the other hand they had a whole grove of chimerica beings living there once.