Personally, I think it is a mistake for organizations to offer "sensitivity training". We need insensitivity training: not training in how to be rude, but training in how not to be sensitive to slights, real or imagined.
When I have expressed this view on a university committee I serve on (a committee charged with advising our administration on religious matters -- I was tapped as the most visible Orthodox Christian on campus), a few of the more vocal (and left-leaning) faculty members on the committee expressed approval, while the one administrator who serves on the committee disliked the idea. (More proof that the rot in academe is concentrated in university administrations, but I digress...)