[Disclaimer: I am not a fan of Doctor Who (probably last watched it in 1989), which may disqualify me from the right to comment in the eyes of many but… ]
Say “Doctor Who” and we ‘see’ men (Tom Baker; Matt Smith; David Tennant; Peter Capaldi; and the others). TV history, every regeneration, dating back to 1963 says The Doctor is male. It is simply a fact of popular culture. So our brains make automatic associations. Dr Who = male. Companion = female (mostly).
The (limited but loud) outcry from those who feel let down by the BBC’s decision to make the Time Lord a lady may reflect the discomfort we feel when our brains' pre-programmed settings are challenged. Even those who celebrate the first female Doctor, will need to adjust their [pre-]sets (pardon the pun). Re-programming takes time, even when we want to do it.
The core question is how do we decide who gets a role? And whether that be as a legendary TV character or something more workaday, the answer seems clear: select the person who best meets the required competencies for the job. Objective, criteria-based selection. The potential problem is that, unless we are careful, we embark on the recruitment process with a pre-set picture in our mind of what the best person looks like. Then, unconsciously, we tailor the criteria to the person. There’s some good research on this (https://ed.stanford.edu/sites/default/files/uhlmann_et_2005.pdf) from Yale University.
Recently, in Singapore, a participant at the end of an inclusion session asked me - ‘Are you saying receptionists do not have to be female and between 25 and 40?’ So strong was the ‘picture’ of what a ‘receptionist’ was in their mind that it had become part of the selection criteria. I asked what aspect of the job required it.
What makes a great Dr Who? Look - I honestly don’t know what the criteria are for that iconic role. But I think that question’s the right one to ask. Figure out the competencies first. Once you have those you are far better placed to hire the person who best meets them... the right person. And you may find that he, or she, looks quite a bit different to the people who usually do that role.
If someone wants to tell me ‘being male’ is a genuine objective requirement for The Doctor - I'd push back quite strongly - I'd want them justify their view. I’d ask "why" a number of times. And I'm fairly certain that “because Doctor Who has always been a man” wouldn't cut it as a response of itself. Move the conversation into the tech sector, financial services, and the upper echelons of many law firms and you can see where I'm going with this.