The announcement has been made, and the role of the 13th Doctor will be played for the first time by a woman, British actress Jodie Whittaker.
Internet entertainment sites seem full of people making fun of male fans who complain about casting a woman, although to be honest the profile of the complain posts seems quite a bit lower than that of the mockers up to this point. For my money, Hayley Atwell would probably have been the right choice, but her time as Peggy Carter in the Captain America movies and the Agent Carter television show may have made her too identifiable with another role for the comfort of the producers.
Whittaker has a number of things going for her. For one, she's 35 and in the BBC-TV video announcing her she definitely looks like a grown-up. Since the series returned in 2005, the most disastrous run has been the whiny emo 11th Doctor played by then 26-year-old Matt Smith. Stories about the Gallifreyan Time Lord work best when he -- and now she -- can project some aura of authority. They also have worked best when the Doctor's relationship with his -- and now her -- Companions is a bit parental. Smith's mopey crushes on his female Companions rang false with the character no matter how well he acted. Although the arc which has him marrying Companion River Song is an excellent example of how not to write a Doctor Who story, that's not really Smith's fault as much as the writers and showrunner Steven Moffat.
Whittaker also has some good credits behind her, most notably the dramatically weighty part of Beth Latimer on the BBC series Broadchurch. The mother of a murdered child is not an easy part to play, and had she done it poorly the series would not have been the hit it was.
Ultimately, the gender of the actor who plays an alien being able to move around through time and coincidentally takes on a new form every time the actor involved quits the show is probably not important. If new showrunner Chris Chibnall, who worked with Whittaker on Broadchurch, understands that, then there's no reason Whittaker can't do well in the role. If Whittaker is simply the Doctor and projects the same level of authority that most of her male predecessors have done -- something women do all the time, on and off screen -- then complaints about her gender really will prove to be silly.
If, on the other hand, she is the Female Doctor, and her existence as a woman after 13 previous regenerations as a male is Something Very Important That Will Teach Us All, then Whittaker's casting is simply self-righteous virtue-signaling and will be a significant burden for her and the show's writers to overcome. Paul McGann holds the title for the least amount of time playing the Doctor, working primarily in one 1996 television movie as the 8th Doctor. If Chibnall and other producers cast Whittaker solely to Make a Statement and they follow that up by paying no attention to what makes the Doctor the Doctor, then there's a good chance she'll compete with him.