To expand slightly: I've had the good fortune to live in three different countries and learn two languages beyond my native (American) English. [parenthetical adjective due to being married to an English woman] Many readers of this forum have no doubt also picked up their cross-cultural awareness informally unless they were wise enough to seek it explicitly.
Regardless of how one attains it, I believe that CQ is valuable of course in culturally diverse groups. But also even in a "domestic only" group or domestic-only-same-gender group, since the moment there are two or more people on a team there are different perspectives and experiences at the table. I believe one becomes a better listener/planner/anticipator / meeting-facilitator through CQ.
If one hasn't acquired it through the good fortune of a semester abroad, work-abroad, or immersion travel/volunteerism, it's never too late to start. And if concerned about carbon-footprint, seek out cultural immersion experiences close to home: for example help out with immigrants who are learning your local language, or such.