This thread is really interested to me, so here's another post. some of the other writers have brought up a very salient point--not everybody is exposed to people of other cultures.
I grew up in a very homogeneous small town in PA. My high school had 2 Black families (they were Colored back then), 1 Jewish family (who could tell when their name was Miller), and no Hispanics, Asians, or anything else that we knew of. My family, especially my father's side, were basically rednecks, but thankfully I did not absorb their influence.
When I went to college, my roommate was blind and Jewish, and his Mother took me in almost as her own. I met people of many, many ethnic extractions while there. When I moved here to Philadelphia in '76, I was exposed to a cosmopolitan cultural (yes! Philadelphia!!), and a city that is 40% African-American, and a good percentage Hispanic. Working in nursing, you really are exposed to numerous cultures just because of the variety in the workforce. Along the way, I picked up passable Spanish, and American Sign Language. (learned Braille in college).
One of my favorite things to do is eat at one of our many Chinese Buffets, and any time you go there you will hear English, Chinese, Spanish, Russian, Arabic, Creole, Greek, etc, etc. So many languages, so little time!
I think exposure is the best cure for the cultural competency issue.