I have no issue with using monsters from all cultures, although nowadays I prefer using published adventures.
Interesting monster are interesting regardless of culture, and D&D is already a hodge-podge of folklore, sci-fi, misconceptions and stuff Gygax et al. made up.
But yes, I try to tie them with the current setting. In my current setting, for example, the major deity is the Lord of Water; it replaces the Catholic Church in all myths that are related to this religion.
I like monsters to make a coherent whole somewhat. For example, all aberrations come from other planes while monstrosities are beast warped by magic, etc.
I'm currently writing a book on Brazilian folklore and it think those monsters could be used anywhere (although many are specific to rivers or forests). It is not always easy to stay true to the source material and usable at the same time (many monsters are a single individual, for example), but I think it is worth the effort.
We've got were-anteaters, flayed tapirs, demonic sows, alligator witches, fire-breathing goats, giant sloths, burning anacondas covered in eyes... cool stuff!