The Westernization of Zen is a common topic in the Buddhasphere (blogs and discussion boards) as well within my own sangha.
Like many American zen groups we are overwhelmingly white and middle class. There is some diversity but one hand could count the members who grew up in a Buddhist family culture.
We look for opportunities to reach out and make contact, we also have been trying to incorporate some of the more traditional holidays and such.
It can't be unique to Buddhism yet to me it does seem different from other religions (and yes although I still consider myself atheist and Zen in no way dependent on supernatural beliefs I call it a religion) in how it has moved from culture to culture.
Each culture from India to China to Japan and now Europe and North America has taken the practice of Buddhism and like the Buddha advised used it to find their own way along the path.
In North America, and I think Europe, the existence of a lay practice is very different from the more monastic focused organizations of the East. Not wrong or right just American Buddhism.