Professor X is a one-off joke on continuity-obsessed fans that turned into a decades-long continuity obsession because the writers are worse than the fans.
The BBC sci-fi show Professor X started the day of the Kennedy assassination. The main character, known as just The Professor despite being credited as Professor X in most of the episodes, was played by a succession of goofy character actors and kiddie comedians. He traveled through time and space with various companions, mostly young human girls in short skirts. In the later years, he always had question marks on his pyjamas. There were a number of recurring enemies, especially the two cyborg races the XTerminators and the Cybertrons, but also aliens like the Snow Vikings, the Automats, and the Super Intelligence.
In 1989, Professor X was canceled. Despite that, and despite all of the best early episodes being missing, it still had a vibrant fandom. Every geeky or gay character in the Doctor Who books was a fan of Professor X. Even Benny got to see it, and enjoyed it because the Seventh Professor was a lot like the Seventh Doctor, but not as dark and with more spoon-playing. Of course the novel series Professor X: The New Adventures featured a darker Seventh Professor, with less spoon-playing. And then there was a movie that was supposed to be the pilot for a new TV series, but it got bad ratings in America. In 2004, a new series was announced, and fans argued about whether the new Professor was the Ninth or Tenth because there had already been a webcast Ninth Professor. Professor X hasn't been mentioned on NuWho or in any of the novels or audios since it started. Presumably the Whoniverse version of Russell T. Davies ruined it forever, and only the Whoniverse version of Gary Russell still cares about it.