Mayor Bill de Blasio is theoretically correct: Rachel Noerdlinger should not be judged by the words or deeds of others, including her live-in boyfriend.

But when the boyfriend is a convicted killer and drug dealer who called police "pigs" in online postings; when she failed to disclose their relationship to the city as required; and when her 17-year-old son has tweeted that, "I am convinced all white people are the devil," one does begin to wonder:

How can Noerdlinger remain as a mayoral adviser and the $170,000-a-year chief of staff to de Blasio's wife, Chirlane McCray?

What makes Noerdlinger, a former Al Sharpton spokeswoman, so valuable that the mayor is willing to risk his integrity by maintaining that the Department of Investigation "found no evidence of intent" to deceive City Hall?

What makes Noerdlinger so valuable that the mayor is willing to risk the appearance of a double standard after her son and boyfriend posted vile comments?

In NYC political circles, it's well known that former Fire Commissioner Salvatore Cassano was not considered for a job by de Blasio because of bigoted postings by his son, now a former emergency medical technician.

What makes Noerdlinger so valuable that the mayor is willing to risk further straining his relationship with the police department?

"She will serve as long as Al Sharpton wants her to serve and she will leave when Al Sharpton decides she can leave," a top law enforcement official said.

That harsh, perhaps simplistic, assessment reflects the anger of police officials at de Blasio and increasingly at Commissioner Bill Bratton. As retired Sgt. Mike Bosak, the editor of a law enforcement newsletter, put it, Bratton has failed to "man up" to the mayor over Sharpton's influence at City Hall.

As for the NYPD and Sharpton, the mayor still doesn't get that it is a zero-sum game.

It's not enough for him to be at a recent dedication ceremony for Bratton's late aide, Jack Maple. Or for his spokesman to say, "The mayor has nothing but the strongest support for the brave men and women of the NYPD," when the mayor then told reporters at last week's 60th birthday bash for Sharpton that, "The more people criticize [Sharpton], the more I want to hang out with him."