To gauge the reaction of a segment of the fans, you’d think someone had stated the next Doctor would kill puppies and kittens regularly on every episode in the new season while making uncomfortable eye contact with the audience. The fans were up in arms stating that this was “Moffat making things up” and would “ruin the show” the problem is they gave little explanation on how the later would be the case and the former is entirely made up and not factual. This is not the first time this has been mentioned and fans have had similar reactions to other suggested potential changes raging against the "SJWs" (an acronym I'm incredibly tired of hearing). There is a kernel of potential truth in SOME of the arguments but others are patently false so I’m going to try and unpack this and deal with the underlying issues.
First let’s discuss the “canon” of gender swapping Time Lords, modern Who fans have a very specific idea of regeneration. It’s seen as a violent and random act with ongoing repercussions that could linger for episodes (or even an entire season as is the case with the Fifth Doctor Colin Baker who was left quite mad by his regeneration to the point he tried to kill his companion or the 12th Doctor who’s regeneration sparked an emotional fallout that changed the nature of many of the relationships he had built prior to his regeneration). The Doctor’s regeneration cycle was anything but normal, it’s been hypothesized since his first regeneration (one brought on by an attempt to continue the series despite the failing health of the lead actor) was forced on him by the Time Lords as a punishment it disrupted the rest of his regeneration cycle. Other prominent regenerations like the regeneration from the 5th to the 6th or 10th to 11th Doctor were particularly violent and disruptive (both involving poisoning). Colin Baker’s Doctor started by almost killing his companion at the time and was at best “unhinged” for the entirety of his time in the TARDIS. Other times, like the regeneration of the 3rd to the 4th Doctor, was quite peaceful but still utterly random in nature.
We’ve only been shown two other Time Lords or Ladies regeneration cycles during the show, the first being that of the Master. By the time we met the Master he had already burnt through most of his regeneration cycle and a large arc was him stealing regenerations with him as a burnt looking monster for a good portion of his run in the series then later stealing bodies and being resuscitated using unknown rituals and eventually his transformation from the Master to Missy (possibly at the same time that the Doctor’s regeneration cycle was rebooted).
The other regeneration cycle we’ve seen though has been much more controlled and methodical. Time Lady Romana regenerated from her first body to that of Princess Astra (due to the dissatisfaction of Mary Tamm and the damsel in distress direction the plots were taking at the time). For her this process was like changing clothes, she tried on several different bodies and even switched species before settling in to the body of a person she had already seen (setting the stage for Colin Baker and Peter Capaldi’s turns in the TARDIS). It could be argued the process is as much a manifestation of the Time Lord’s personality with the Doctor and the Master both being very chaotic in nature while Romana was very in control (and one of the few people to ever give the Doctor as good as they took from him).
In the story Shada an episode written by the amazing Douglas Adams but cut from the 17th season due to labour disputes there is a line referring to the Corsair, a Time Lord who swapped genders. Later during the regeneration in to the 11th Doctor Smith’s Doctor says that maybe he was “a girl” given his long hair at the time. This all sets up in canon the potential for variations never before explored.
So, the argument that this is “Moffat” making things up just doesn’t hold water. Yes he’s brought it up more than prior show runners but this goes back to the era of the 4th Doctor and was written by none other than Douglas Adams! This is something that cannot just be shrugged away.
This brings us to the second and actually valid argument, this will change the dynamic and compromise the structure of the show. This is true, the show’s structure for over 50 years now (not taking in to account several of those years were spent with zero new content) has been based around the Doctor and his relationship with his companions. The Doctor has and a variety of personas including cantankerous old man, clown, smooth kung-fu magician, mad man, nice fellow who really likes celery, even more mad man, kind of evil scheming dude who seemed nice on the surface but wasn’t so nice underneath, warrior, PTSD sufferer, smooth operator, again a clown and reset to cantankerous old man. In each of these his relationship with his companions has been central to the structure of the story. With Hartnell’s Doctor you had someone who was downright hostile to his companions. When he wasn’t condescending he was actively putting them in harm’s way or just disregarding them entirely (even his own Granddaughter) while Pertwee’s Doctor was a smooth operator who easily flirted with his companions while always assuming the moral authority.
Baker would try and scam and scheme and be generally mad as a hatter while Davison’s Doctor actually cared and would often put his companions before himself (something none of the Doctors before and none of the Doctors in the classic series after would really do).
In the new Who you again have a protector in Eccleston, a flirtatious gadabout in Tennant, a foppish clown in Smith and a stern task master in Capaldi and their relationships have reflected this entirely. Rose and the 9th Doctor never truly bonded, yes they were tight but she was more enthralled with the adventure while with Tennant they fell in love and she literally gets to live happily ever after in a pocket dimension with his hand. Smith’s Doctor and the Ponds had the feel of “my crazy cousin” there was some initial romantic tension but that burnt off quickly to the point where they appeared as if they were tolerating him and not particularly enjoying themselves. Meanwhile Capaldi’s relationship with Clara has been downright hostile at times. To say it was condescending would be condescending to condescension.
Now if you flip this dynamic you have two constructs which are most common in film and television, the mother and the bitch. The mother is protective and nurturing (and the Doctor’s often had the father archetype applied to him) while the bitch is domineering and cruel. Capaldi’s Doctor has displayed many behaviours that if parsed on a female character could be classified as the “bitch” while Tennant and Smith have many behaviours that could have fit in the “mother” category. The problem for many viewers is this becomes a point of access, the father figure is a powerful attachment point for them and seeing this dynamic changed becomes difficult for them to grapple with. If the companion is male will there be sexual tension? Will there be sexual tension with two females like Jenny and Madame Vastra? (Which would be a double whammy of issues for a lot of viewers.) The problem is after 50 years of the Doctor being constructed in one pattern they are afraid of the change and suspect it will undermine the show.
They have a right to be concerned, this reeks of stunt casting. Messing with the formula for the sake of “mixing it up” is like adding a new kid to a family sitcom. It is Shark Jumping programming at it’s most foul, what they don’t understand is it doesn’t need to be. Moffat (for all the hate people heap upon him) has been very good, he’s had a lot of writers pen scripts that have helped flesh out the mess Davies made of the series on his return. He’s brought new viewers and over the course of his time with Smith opened it up to entire generations of kids who may not have been interested in the show before and presented nuanced characters with depth. He may well not be at the helm when this happens but who’s to say the BBC would hire someone who was not equally as competent? Further viewers are failing to see the problem that they are succumbing to tropes, they see women as falling in to archatypes but women in film can be as complex and nuanced as men when it comes to storytelling and they are preventing themselves from experiencing an entire host of stories told in a way that has never been done before in the Who setting. They argue about making a spin off with a different Time Lady or making the Doctor of colour as if that is some kind of trade off, but the reality is if there are good stories to be told they can be told and this is the same kind of backwards logic that video game designers use when they say "games with females don't sell".
Could it wreck the franchise? Yes, it sure could just like adding the romantic subtext for several years between Tennant and pretty much every companion but Donna (who ironically had the relationship most like an old married couple). Guess what though, the romantic element added poignancy to the story and brought the series in a different direction highlighting the conflict the Doctor suffers and the fact he is at times blind to the emotions of others. Nuance and depth that was not there before. Just like that, the change of gender opens up a host of stories and possibilities and the opportunity to transcend tropes and stereotypes in new ways that aren’t just flipping them to make the woman tough or cruel or matronly but actual nuance and depth.