I absolutely think something can be sexist and part of a culture, you really don't? Christians in the US rallying against birth control, abortion, hell even women in the workplace/military etc? Surely you can't be that partisan?
Women's rights are definitely one of the issues I fall in the left end of the spectrum. Women should be held in equal standing to men (and currently they are not), men shouldn't dictate what women do with their bodies, their place is not in the home making sandwiches raising kids, and I don't care if that's what the cultural norm is. How people can claim to be both for women's rights and also for things like the burka which is a cultural enslavement of women is beyond me.