The thing is that regeneration as a concept is complete fairy tale bullshit if you think about it longer than two seconds. Sure, I can buy that there's some alien process that turns you younger, but something that randomizes your physical features, bone structure, hairstyle, PERSONALITY?
At that point, switching genders is absolutely not a stretch.
Sorry but I dislike this way of thinking. "It's unrealistic so we can make anything happen." By that logic, since the TARDIS is utterly absurd, let's have the Doctor turn into a Dinosaur that shoots eye beams and flies through the air.
That is not a good attitude to have when writing sci fi and fantasy in my opinion. You still need laws and limitations even in something like Doctor Who as that's what gives it an identity and stops it from being a parody.
Meanwhile I have NEVER understood this argument that people give of "you can change height, hairline, bone structure but not gender? Why."
YOU have changed your hairline, your bone structure and yes, your personality too! Are you the same person in any way now that you were when you were ten? Every cell in your body changes every 7 years. Regeneration can be seen as a similar process, only more rapid and more extreme, but it's the same basic thing.
However gender is clearly a lot bigger a thing to change, since only 0.1 percent of the population do it, and those who do change gender, DO feel like they've become a completely new person. (Hence why dead naming them is seen as a nasty and spiteful thing to do.)
Adding a gender change to the concept of regeneration is a terrible, terrible idea because.
In the original all of the Doctors were meant to be the same person under the new face. Whilst their outer persona's were different, they all followed a template to their core personality that was laid down by Hartnell's performance. IE the key to getting the Doctor right in Classic Who was in getting someone who would in some ways be different and make it their own, but not so much you could never imagine it was still Hartnell under there.
Now New Who admittedly broke this from the start in regards to being believable as Hartnell (hence the controversy), BUT I think it got away with it because Eccelston was the first Doctor in 2 decades. I'm not saying Classic Who was forgotten. I myself am someone who discovered it in the 90s, but obviously due to simply not being on tv it wasn't as mainstream, so new who put it back in mainstream popular culture again, therefore for many Eccelston was their first.
Even then however, Eccelston, Tennant, Hurt, Smith and even Capaldi I feel were still believable if you will as being the same characters as each other (with Matt adding elements of the classic template, perhaps explaining why he is the most popular Doctor overall of the new who boys as he bridges the gap.) There was if you will a new template for the new who Doctors like there had been for the classic era Doctors, one laid down by the 9th and 10th Doctors that the others followed. (Ironically perhaps a bit too closely, or maybe there just wasn't as much in the new template as there was in Hartnells?)
Still either way that is basically how to do DW and regeneration. Create a template and then stick to it, whilst also varying it within the template. If you make them all completely different with no similarities, then the Doctor becomes just a title passed down to other characters. The fact that he seems like one character is a key to its success, as it causes people to keep watching when their doctor is gone.
Compare DW's longevity to Primeval that never recovered from losing Douglas Henshall. Even though I love Jason Flemying (who would have made an excellent Doctor btw in the mould of Pertwee.) When Henshall left all the story arcs, relationships and characters that were tied up in his character had to go with him and for most Primeval lost its identity. Hartnell to Troughton however? They could keep up things like the Daleks, his companions, Cybermen etc and even Hartnell's development which made the transition smoother. Ditto Jon to Tom.
With this in mind a woman is just too jarring coming after either template, both of which were firmly male. The only way you could get away with it, is if you had another hiatus and then the first of the new batch was a woman, but even then you'd need her to be in a different canon I'd say. Still whilst that would be more practical, I still don't think it would be a particularly good idea, because ironically as someone who clearly LOVES female heroes, I'm not interested in a novelty female version of a male character.
I actually think any producer who would cast a woman is a dickhead to be honest, because they are putting the actress in such a difficult role. There's no way she could play it.
If she tries to be feminine, then she will stick out like a sore thumb and jar from the men before her, simply because they were men. Not saying a woman couldn't play a hero like the Doctor. Men and women can play all of the same TYPES of heroes, but again this isn't a case of playing the same type of hero. Again you're having to imagine that is Hartnell now applying make up to himself, wearing a dress etc. That's a bigger leap than him simply becoming younger or a bit more of a fighter in this big body, or his tastes becoming a bit fancyer. If you have it that he can change that much, it becomes a slippery slope that anything about him can change. IE you can't say don't have the Doctor shag Sarah, if he can become a woman now as the response to that is "well if he can go from William Hartnell to Paloma Faith, why not get a sex drive?" Then it just keeps going and going until the template/his character is gone.
If she tries to play it as a trans person IE someone who wants to change to be the gender they are comfortable as, then that also jars as clearly that's not who the Doctor is, and also I think trying to equate it with transgenderism as idiots like Elizabeth Sandifier did, is harmful to trans people. What happens when the Doctor changes back into a male, which will happen sooner or later? You're basically giving trans people this icon and then snatching it away from them.
If she tries to play it as someone gender neutral, IE lets strip any and all femininity from her just to make her not jar with the men, then your question becomes, why not just cast a man in the first place? Don't give me the "well she was the best for the part". Really that's why you have to cover up her gender?
Finally if you have it that it's an accident, well okay that might make more practical sense, but even then what's the point? Why have a female hero who is a man trapped in a woman's body and will change back? Not exactly empowering?
Also in the current climate you'll be putting this woman at the head of the culture war bullshit, and you'll also be putting so much pressure on her, because as the first female Doctor she will have ten times the responsibility to be good as any man in the role, because she'll feel more artificial and crowbarred in there.
Jodie Whittaker meanwhile fell victim to ALL of these problems. She openly said she didn't know how to play it, because the previous Doctors were men and she couldn't relate to them, so even she admitted she felt disjointed from the character. At the same time she had to be made as genderless and sexless as possible to fit, which drew criticism with a lot of people saying the female Doctor was pointless as a result, and her being given an awful, unflattering costume, like a baggy rodeo clown. Meanwhile what I said that once something as big as his gender has been changed, it becomes a slippery slope of well anything can change now, which is exactly what happened via the Timeless Children and the furry Doctor retcons in Jodie's time and the eventual deregeneration.
Finally she was also put front and centre of the culture war bullshit too, and said to be flying the flag for all women rather than just playing a role in a tv show like Tom Baker had been.
Thing is Chibnall knew all of these things would happen, but he didn't care. I mean if I could work these problems with a female Doctor out in 2013, so could he. He went ahead with it however for his own ego of being the first man to cast a woman in the role. You could say maybe he was just so ideological he didn't care, but I don't think he is. The guy isn't even remotely left wing or feminist. As we've been over he's a bandwagon jumper.
Hence why his era of Torchwood contains sleazy, exploitative trash as he was trying to cash in on the hotter and sexier fantasy trend of Smallville, Buffy and Xena. (Then there is also Kerblam and his shilling for the BBC. Guy's as left wing as Sargon of Akkad.)
He was just an egomaniac looking to earn his place in the history books and I am so glad it blew up in his face, just like his avatar Whizz Kid trying to entertain the Gods of Ragnarok.
Sadly however Chibbers and Jodie's ineptitude I think is distracting people from the fact that a female Doctor is just a bad idea in general. Yes I don't doubt with scripts by Bob Holmes, and an actress like Paloma Faith, Morgana Robinson or Susan Wokoma in the role, that the female Doctor would have been watchable, but in the long run it would still have caused all of those problems I mentioned. First thing we need to do if we do get an alternate sequel, or prize it from the Fitzroy's cold dead hands, is be strong and say NO FEMALE DOCTOR WHO!