First - when was China at war with US?
Second, I wouldn’t be too nit-picky about the subject. People at that point were still used to Shanghai just being another exotic locale, not a communist territory, which only happened very recently.
From the nineteenth of October, 1950 when Chinese forces crossed the Yalu river and joined North Korean forces until the cease fire in 1953.
So roughly from a year before the movie was shot until a year after it was released.
We were fighting a hot war with China in Korea at the time. Doris’ lover must have found it doubly disturbing that she vowed to head not only for an exotic location but one behind the Iron Curtain.