It is a common term in human services and social work, and I am required to have annual training on some aspect of cross cultural competency. Used to be referred to as cultural sensitivity training. While the concept arose out of race relationships and discriminatory practices, both intended and unintended between Whites and African-Americans, it is now more inclusive. I've had cross cultural training on working with various hispanic nationalities, and southeast Asian populations. LGBT populations are often included.

It is certainly jargony sounding, but I don't know what would not be jargony sounding.