The big question in the NAACP Rachel Dolezal case: Why?

When it comes to family fights, the Dolezal dispute may have surmounted all others with its bitter and bizarre allegations.

Now, the question is what happens to Rachel Dolezal, the NAACP leader in Spokane, Wash., whose parents claim she has faked being black.

The National Assn. for the Advancement of Colored People is standing by her for now.

In a statement Friday, after her parents' allegations were first reported in the Coeur d’Alene Press, the NAACP said Dolezal was involved in a "legal issue with her family."

The group also stressed that anyone can fight for civil rights, regardless of his or her race.

"One’s racial identity is not a qualifying criteria or disqualifying standard for NAACP leadership," it said in a statement. It added: "In every corner of this country, the NAACP remains committed to securing political, educational and economic justice for all people, and we encourage Americans of all stripes to become members and serve as leaders in our organization."

But the question of Dolezal's race, and whether she passed herself off as black, have shown that race does matter in this country, especially at a time of heightened scrutiny over law enforcement treatment of African Americans, and as some states pass voting restrictions that critics say are aimed at black voters.

It's not just the racial issue that has sparked a nationwide debate on Dolezal's alleged misrepresentation, though.

It's the question of identity in general, and at what point a person's identification with a group qualifies her to actually claim membership in that group, said Christina Greer, a political science professor at Fordham University in New York and the author of the book "Black Ethnics: Race, Immigration, and the Pursuit of the American Dream."

"Race and ethnicity are fluid for a lot of people," Greer said. "There are a lot of non-white people raised with whites who identify more as white. She raises the question of can we judge and say, 'You are not allowed to pass as black.' "

But Greer noted that on social media, there also have been comments about other forms of identification, including gender. That has been a major talking point since Caitlyn Jenner, formerly known as Olympic athlete and Kardashian family patriarch Bruce Jenner, introduced herself to the world as a woman.

Twitter was blasted with posts from people arguing over the notion of accepting Jenner as a woman while disputing Dolezal's race.

But across social media, there is clear anger at Dolezal, whose critics are asking where a white woman gets off portraying herself as a black woman, including having suffered the racism and slights that black females face.

"This woman has been giving advice, and mentoring black kids under the ruse that she actually understands what they feel like as black kids in America," Ashley Jacobs wrote on the Spokane NAACP chapter's Facebook page beneath a photograph showing Dolezal standing beside a black man. The photograph, posted in January, purported to show Dolezal and her father.

"She was making money off the lie that she personally understood the pain black women face in society," Jacobs wrote. "She had a job 'teaching' about the experience of being a black woman, something she knows nothing about."

Neither Dolezal nor her parents, who live in Montana, have explained the big question: Why?

Why would Dolezal pretend to be someone she is not, and why would her parents come forward now?

Dolezal, who is 37 and who has been praised for raising the NAACP's profile in Spokane, walked away from a TV reporter who confronted her about the issue.

The reporter from KXLY in Spokane showed Dolezal a photograph of the elderly black man whose picture was on the Facebook page and asked whether it was her father. "Yes, that's my dad," she replied.

Asked if her father had come to Spokane in January, as the Facebook post said he would, Dolezal appeared to tense up. She said he had to cancel the trip because he has lung cancer.

Then, when asked whether she is African American, Dolezal replied, "I don't understand the question," and walked away.

Her parents, who were interviewed on CNN on Friday from their home in Montana, said their daughter had been claiming to be African American for years, but they only recently began receiving media queries to confirm she is their birth daughter.

That may have been the catalyst for them speaking out. "We've never been asked these questions until now," her father said.

The couple has four adopted children as well as Rachel. Three of them are African American and one is from Haiti.

Dolezal's mom said Rachel cut ties with them several years ago.

"She doesn’t want us where she is. She doesn’t want to be seen with us because that ruins her image," Dolezal's mom said.

Officials in Spokane and nearby Coeur d'Alene, Idaho, where Rachel Dolezal lives, are weighing what, if any, action to take.

Dolezal has reported to police that she has been the victim of several death threats and other possible hate crimes related to her race over the years — reports that some people are now questioning.

During the KXLY interview, Dolezal spoke passionately about the terror inflicted on her and her sons as a result of the incidents, which she said included finding a noose-like rope hanging near their home.

She denied suggestions she had made up the incidents.

City officials in Spokane are looking into whether Dolezal lied when she listed herself as white, black and American Indian on an application to serve on the police department's ombudsman commission. She serves as chairwoman of the independent commission, on top of her NAACP work, and works as an adjunct faculty member at Eastern Washington University.

"We are committed to independent citizen oversight and take very seriously the concerns raised regarding the chair of the independent citizen police ombudsman commission," Mayor David Condon and City Council President Ben Stuckart said in a joint statement.

"We are gathering facts to determine if any city policies related to volunteer boards and commissions have been violated. That information will be reviewed by the City Council, which has oversight of city boards and commissions."

Times staff writer Christine Mai-Duc contributed to this report.

Follow @tinasusman on Twitter