One of the biggest threats to organisational culture is that of external culture, especially in countries where there are hierarchical norms that are at odds with those of a modern 21st century business.
An often-cited, but nevertheless excellent example of this was revealed by author Malcolm Gladwell in his book Outliers: The Story of Success, in which he described the part that Values inherent in South Korean national culture had to play in the downing of 11 Korean Air commercial planes over the 12 year period between 1987 and 1999.
The normal expected cause: old planes and poor maintenance didn’t apply to Korean Air, leaving Gladwell to theorise that the hierarchical nature of South Korean culture was to blame. South Koreans typically share common Values of deference to their elders and superiors, which came to a fatal and tragic head during a crash of a passenger aircraft on the Pacific island of Guam, when the pilot (the senior member of the flight crew) made an error and the co-pilot (a distinct hierarchical junior) did nothing to correct him, allowing the disaster to happen.
Within your own organisation, the threat of such an awful outcome may not be as real, but the danger of an unwanted outcome when work-mode and life-mode aren’t clearly compartmentalised is nevertheless a danger.