LONDON — Be on the lookout, the British counterterrorism police warned, for young people being radicalized by extremists like neo-Nazis, militant Islamists, Satanists, white supremacists — and climate-change activists.

The counterterrorism police reversed course soon after it came to light that they had published a brochure that lumped the group Extinction Rebellion, not to mention animal rights activists, together with terrorist organizations, retracting the document.

But on Monday, a top government official refused to find fault with it.

“Everything has to be based in terms of risk to the public, security risks, security threats, and that is based on information from the police and various intelligence that we all receive,” Priti Patel, the home secretary, said in an interview with LBC radio.

“That’s the proper thing to do,” said Ms. Patel, one of the farthest-right members of Prime Minister Boris Johnson’s cabinet. “You develop your policing approach accordingly.”