According to this article, the "fixation on cultural sensitivity is changing the debate around female genital mutilation, with a growing number of professors and women's rights activists becoming hesitant to condemn the practice".
My response to this has to be, would they have been, are they still, equally hesitant to condemn slavery? (it still exists, it is a well established tradition in some areas). Would they have had difficulty in condemning foot-binding in Chinese culture?
There is an interesting post on Global Voices about the tradition of over-feeding women in Mauritania where it is sexy for women to be fat. A commenter on an earlier post had said "but it is not their fault, this is how they were educated". Similar arguments apply.
Being aware of cultural issues and sensitivities cannot mean that harmful practices should be condoned. And I notice that the majority of these issues are harm caused to women.