What is the English term that one uses to indicate "the culture one is born in"?
The word 'native' is used to describe anything that applies to you at the time of your birth. So the culture you were born in would be your 'native culture'.
People sometimes use 'native' to mean 'the main thing' (as in "
since I came to England, English has become my native language") but this is wrong.
This blog entry has “birth culture” as its title and then once again near the end to describe the culture of the author’s birth. “Cultural roots” is also used with that meaning near the article's top.
(from Beyond Two Worlds: Musings of a Taiwanese-American Adoptee)
As long as it’s clear that you’re talking/writing about some person’s “native culture” then there would be little chance for ambiguity, but “native culture/s” can also mean [a country’s] “indigenous culture/s,” i.e., the culture of its indigenous/native inhabitants. (Just as, to be fair, “birth culture” should be used with an appropriate personal possessive pronoun to avoid confusion with other meanings of that term, so maybe "cultural roots" would be less prone to confusion)