No, because cultures can only be undermined by their own carriers in a free society.  I can't force people of other cultures to eat pork or cow, or go out drinking every Friday night, or watch profanity-filled movies.  I can't force them to listen to rock music or accept my God (or lackthereof).

There's a claim often made by opponents of globalization that says it will destroy cultures by somehow forcing our culture upon them, and it's nonsense.  People will make their own decisions about their cultures, because cultures are tied directly to our individual and collective fundamental beliefs -- as nations, as families, and so on.  And no one can take away your beliefs.

Whether someone accepts the West's culture or his own is his choice.  But isn't it better to have a choice about such a thing?

Be nice to America. Or we'll bring democracy to your country.