Christopher Eccleston's Doctor Who was actually declared not suitable for kids. After the classic series of Doctor Who was canceled in 1989 and the show appeared to be gone forever, an ill-fated mid-'90s revival starring Paul McGann seemed to have sealed its fate.
But by the early 2000s, a new generation of BBC executives who grew up watching Doctor Who were willing to give it another shot. They hired Russell T. Davies as the showrunner, and they gave him a big budget to work with. Davies spared no expense when it came to casting, choosing Christopher Eccleston as the Doctor and Billie Piper as his companion, Rose. The gamble paid off, Doctor Who season 1 had rave reviews, and the relaunched series is still going 15 years later.
It's easy to forget that, back in 2005, Davies' Doctor Who did receive criticism. This became especially noticeable when it came to releasing the season 1 DVD, and the British Board of Film Classification (BBFC) refused to award it a PG certificate. As far as they were concerned, two specific episodes were unsuitable for child audiences. The BBFC was particularly critical of the episode "Dalek" in which the Ninth Doctor confronted what he believed to be the last survivor of the Dalek race. This Doctor had been left emotionally traumatized by the Time War and was still reeling from his decision to destroy both the Time Lords and the Daleks. As a result, "Dalek" was a tense psychological drama that explored PTSD, and it saw the Doctor shift into a far more ruthless form when he pulled a gun on the Dalek.
The BBFC felt that "Dalek" went too far. "We were concerned at the use of violence to resolve problems," they observed. "The Doctor is a role model for young children, but he takes out his cruelty on the Dalek. A good role model should not use torture to satisfy his desire for revenge." This criticism was frankly surreal, given the episode's emotional climax saw the Doctor realize he had lost his way when he was told he would have made a good Dalek.
The BBFC was also concerned about the episode "The Unquiet Dead," in which the Doctor confronted wraith-like beings who were victims of the Time War, but as James Chapman notes in his book Inside the TARDIS, they were bizarrely untroubled by episodes such as "The Empty Child," which featured reanimated corpses. However inconsistent the BBFC may have been, they awarded Doctor Who season 1 a 12 rating (roughly the same as a PG-13 in the U.S) because of these two episodes, indicating they didn't feel the show was suitable for children.