It depends what you mean by “change the halacha”.
It won’t change the underlying halacha, but can change the applicability.
Examples:
Lo silbash. Western styles have some influence on what’s considered beged isha.
Hocheach tochiach: someone influenced by Western culture (we all are to some degree) might be influenced better by certain means than someone raised in a different culture. This is related to the potching issue as well.
Bein adam l’chaveiro (including sholom bayis). If people in a certain culture are offended by certain things which aren’t considered offensive in a different culture, you shouldn’t subject them to it. For example, Israelis have certain tough mannerisms which are considered rude in the USA (they probably consider us soft).