I mean I would think so, but I do not think gender specifically would be a problem if it was handled correctly.
With Bond, the change is either a semi revisioning or just something everybody winks at.
Wit the Doctor there are maybe ways to work it, but part of the issue, IMO, is how it was done. It was very much done just because and sort of tore everything around it down to make it happen. And then threw out alot of other cannon along the way with little regard.
If you have the right actor, the right storytelling and respect for the material than there is not a reason it could not work but none of that happened with Dr. Who.
I am not a big Bond fan, so I cannot comment on it really.
Just saying that htere is nothing wrong with a white British male being either the Dr or Bond, but in this PC climate of today, must get minorities and other gender forced into the roles!
Mickey Mouse owns marvel, so pretty clear why there has been a mandate to clean and sweep out all white males, as must have females and minorites exclusively now represented!