Cultures are beautiful, and they grow and develop best when allowed to intermingle with others.
They stagnate and die when cut off and insular.
Me, I favor a "Cultural Free Market". Let everyone pick and use the best parts of cultures that work best for them and let our cultures flourish, grow, and mix into new and exciting cultures and subcultures.
I'll continue cooking Mexican food, praying Persian prayers, watching Japanese shows and Indian movies, making Latvian artwork, reading Chinese books, dreaming French philosophy, playing American games, and listening to Mongolian music.
And those who are horrified by the idea of cultures growing in this way can feel free to watch their own traditions wither and die. Culture is a changing thing, and clinging to stasis will never work, especially in this case.