Basically how christians have always operated since they first emerged and started doing the same throughout the hellenic world. Most (all?) christian traditions are pagan in origin. The main goal was not necessarily replacement but a sort of corporate ownership takeover of the littany of existing traditions, such that these cultures might be ingrained into a unified fold of christian power/influence/customs/laws/expectations and not see themselves as some distinct independent people. And boy that model worked to tame europe and much of the known world under the whip of the pope in a way the roman emperors never could, at least until Martin Luther screwed up a bit of that unity.

Mexico is interesting because it is a certainly a different catholicism than what is practiced elsewhere. Tell a devout old world European catholic about say Day of the Dead traditions and they will probably think its blasphemy. There is a lot of what amounts to local diety worship still as well, although they just label them as some patron saint of somesuch to preserve the veil of monotheism.

If by “America” you mean Meso and South America, sure. The USA, however, was Protestant, not Catholic.

The missing term and concept is Inculturation

https://en.wikipedia.org/wiki/Inculturation

Another appropriate word for the colonization of America is genocide.

I'm old enough to remember being taught how America was settled by expanding into the vast wilderness of the continent, and that sometimes they had skirmishes with natives but they found them new places to live.

It turns out it wasn't quite as neat and tidy as suggested.