KingSpeed, if someone were being interviewed about gender roles and I said, "I really don't feel it's appropriate for women to direct Broadway shows or run companies, because they don't have the leadership for it," and then I "apologized" by saying, "Sorry, my remark was insensitive, I don't really feel that way. As far as I'm concerned, whatever you want to do, GO FOR IT" -- would you accept that apology? Of course not. The only sincere apology in that case would be, "I am sorry that stereotypical gender roles have been so ingrained in me that I made a terribly offensive remark. I will work to re-wire my brain and move beyond my conception of stereotypical roles."
Do you see the difference? People shouldn't apologize by lying about their true feelings. Rather, they should admit that some of their feelings and beliefs are wrong and hurtful and ignorant, and they should apologize for THAT and then work to overcome those feelings. That's the kind of apology I, for one, would accept.