Note that this is just based on my literary-socio-psychological observations, so it's quite possible we'll disagree here.
Look at Tolkienesque dwarves - they are not just people, they are humans.
Elves? Same.
Even the dragon, which is supposed to be quite different, can't help but end up as a human with quirks and traits, as he was written by a human.
Now, let's look at the concept of religion, or specifically, religiosity and atheism. Our current concepts of such in Israel are not only Western, but Christian for these terms. That caused an issue in Israel when immigrants from Arab countries were presented with terms couched in an alien framework.
Finally, I'd like to bring up the discussion we've had previously on conditioned sexual attraction in our own lives.
The analogy is this, that regardless of our own genders, the framework in which we see people and society is gendered. Trying to either a character and/or a society that is different, that is not gendered, is going to be really hard, and for a case of a show with multiple episodes and writers, all but impossible.
Is it possible as an idea, sure. Do I think most people who are already over 20 years old be able to do so? I don't think so. And I'm thinking of most sci-fi authors as well. "Gender" at this point is not just a trait of people, but one of the lenses we view the world through, regardless of how we apply the trait itself. And that'd require a cultural shift to shake off, and those take quite some time. Decades.
Edit: Realized it might be a bit of a semantic disconnect. When I say The Doctor will be "gendered", I don't necessarily mean either "man" or "woman," but that it'd be part of the gendered framework, and with gendered aspects.