I think in games with fully voiced games it could be a 'problem' as in 'more expensive', when you can choose between different pronouns. On the other hand, DA:I even offered two completely different voices for each gender. When it comes to character customisation, I see no reason to block one hairstyle from being used with a different gender, though.
Such changes in a mindset is not easy and takes a while, I guess, since we are so used of thinking in easy terms and pigeon-holes, like black and white, good and evil, wrong or false, man or woman, and so on and so on. Having broken up this simple paradigm is quite the thing for many people, because they have to change and their former world picture is questioned and challenged; you are kind of telling people that they were wrong, and people usually don't like to be told that they are/were wrong. Damn, I know many people when you criticise something with good intention and in a polite way to improve their work (or something else) and they take it personally (for instance with less subtlety, "Don't tell me!" "Don't tell me my job!" or with killer phrases like "We did it like that for the last 10 years and that's that.") For some people it really seems to mark the end of the world.