Whiteness has become “toxic” under schools Chancellor Richard Carranza’s regime, insiders charge.

At least four top Department of Education executives who have been demoted or stripped of duties under Carranza’s sweeping reorganization are poised to sue the city, claiming he has created “an environment which is hostile toward whites,” a source told The Post.

The women — all white, veteran administrators — contend they were pushed aside for less qualified persons of color.

“These decisions are being made because DOE leadership believes that skin color plays a role in how to get equity — that white people can’t convey the message,” said a source familiar with the complaints.

“There’s a toxic whiteness concept going on.”

Davida Perry, managing partner of Schwartz Perry & Heller, a law firm focusing on employment discrimination and sex harassment cases, represents the women. She declined to comment pending the filing of the suit, which is expected within two weeks.

Under Carranza’s leadership, sources said, whites, in some cases, are being told they must give up power or lose responsibilities no matter how well they have performed.

More than a dozen high-ranking superintendents and deputies who had served under ex-Chancellor Carmen Fariña have been demoted — some with large pay cuts — or pushed into retirement, sources said. Others have lesser duties and new bosses.

“Since Carranza took office, he’s brought in a lot of new people. As a result, it’s been bureaucratic chaos and backbiting, with deputies and their subordinates seeking better perches in the pecking order,” said David Bloomfield, a Brooklyn College and CUNY Grad Center education professor.

“Racial tensions appear to be one manifestation of these internal battles.”

Meanwhile, the DOE has spent hundreds of thousands of dollars on consultants to coach supervisors on how to “disrupt the power structure and dismantle institutional racism,” a supervisor said.

“There’s been a lot of discussion of white supremacy and how it manifests in the workplace, conversations about race, and looking at how the white culture behaves,” said a white executive who received the training.

“White supremacy is characterized by perfectionism, a belief in meritocracy, and the Protestant work ethic,” the exec said, adding that whites who object when accused of deep-rooted bias are called “fragile” and “defensive.”

“Can you imagine if we scrutinized blackness or brownness? We’re being trained in anti-bias not to stereotype blacks, but they’re fostering a stereotyping of whites.”

Besides the four administrators who have signed up to sue the city, others may file Equal Employment Opportunity discrimination complaints, insiders said.

Several of the women work in Carranza’s new School Climate and Wellness division led by his appointee, deputy chancellor LaShawn Robinson.

That division includes the Office of Equity and Access, led by senior executive director Ruby Ababio-Fernandez, appointed by Robinson. Both women are African-American.

The office has adopted “Courageous Conversation,” a protocol for training on racism in the workplace founded by Glenn Singleton, the president of Pacific Educational Group Inc.

The DOE has contracted the company for $775,000 in services, paying $582,603 to date, records compiled by the City Comptroller show.

Singleton’s protocol defines racism as: “Any act that even unwittingly tolerates, accepts or reinforces racially unequal opportunities or outcomes for children to learn and thrive.”

“Whiteness” is defined as: “The component of each and every one of ourselves that expects assimilation to the dominant culture.”

The outline states, “It is not talking about these issues that create divisiveness. The divisiveness already exists in the society and in our schools. It is through dialogue, even when uncomfortable, the healing and change begin.”

Another consultant hired by the office is Darnisa Amante, CEO and founder of Disruptive Equity Education Project, or DEEP. The DOE has contracted the outfit for $175,000, paying $54,200 so far, records show.

“We work together to change mindsets around equity and dismantling systemic oppression and racism,” Amante is quoted on the DEEP website.

“They’ve trained people in these approaches — interrogating whiteness, examining its relationship to power and privilege,” said the DOE exec who had training.

“The intent is to create a shared understanding. They believe this is positive and helpful. But it’s resulted in a hostile environment where whites are subject to being criticized, belittled and harassed. It’s divisive, and has fostered disharmony.”

Bloomfield, the professor, called the efforts a minefield. “Anti-bias training often exposes these tensions, but in some cases leaders have not been adept at handling the raw feelings.”

Carranza announced a DOE restructuring last June, several months after he moved to NYC from Houston, where he was schools chief. He created a new bureaucratic layer of nine “executive superintendents” who cost at least $2.5 million a year in salary and benefits.

Carranza also ousted or reassigned several executives, both white and black, for performance issues. However, some who retired had stellar records. Bonnie Laboy, the 53-year-old superintendent of District 2 in Manhattan, led many of the city’s highest-performing schools. She now works as a consultant in New Jersey.

District 2 is a bastion of affluence with selective schools that admit fewer black and Hispanic kids. Carranza has blasted the “screens” as “segregating our schools.” The district has a modest diversity plan that sets aside up to 17 percent of seats in three top middle schools for kids from poor families.

Insiders believe Laboy was pushed to leave or chose to bow out rather than oversee a heated battle over admission changes.

“She knows it’s going to be really, really ugly,” said Shino Tanikawa, a District 2 parent leader and member of the DOE’s School Diversity Advisory Group. “I think she decided it’s not what she signed up to do.”

Laboy could not be reached for comment.

The DOE dismissed complaints that it has discriminated against whites.

“We hire the right people to get the job done for kids and families, and any claim of ‘reverse racism’ has no basis in fact,” said spokesman Will Mantell. “We’ll continue to foster a supportive environment for all our employees.”