Whatever "cultural diversity" is about, it has to mean accepting and welcoming a wide range of cultural activities from all ethnic backgrounds. Morris Dance is an excellent example of such. You can't get much more diverse culturally than Morris Dancers.

If "Harriet's criteria about how society should be run in terms of cultural diversity" aren't consistent with that meaning, the term would be clearly a misnomer, since it would imply an effort to eliminate cultural diversity.

I rather suspect that cptsnapper is putting a somewhat misleading spin on whatever Ms Harman might have said or written in this context.