The issue of black inequality has been front and center in the national dialogue for weeks as protests rolled out nightly, but now the conflict has ignited in the heart of the protest movement itself.

With each new demonstration against the killings of unarmed black men by white police in Missouri and New York, questions — and in many cases, objections — proliferate about the role of white voices in a movement that centers on African Americans’ grievances.

The issue arose out of protests in Oakland, Berkeley and San Francisco where, night after night, there were more whites than blacks. Some black leaders say they are spending their energy organizing for action away from the streets. Others believe some African Americans are afraid to participate in protests in which small fringe mobs turn violent — putting black people in danger of the very thing they’re protesting, attacks by police.

“There are people who would like to participate, but they feel co-opted and don’t want to be aligned with the vandalism and with people throwing things at the police,” said Alameda County Supervisor Keith Carson, a black community leader who has participated in numerous social movements over the years. “It’s a small number that causes the trouble at the protests, but we just don’t know how to overcome that. The same issue co-opted the Occupy movement.”

Carson said he welcomes white voices and participation. Many African American activists say the same — but they also say blacks’ voices need to be in the forefront.

'Hand over the bullhorn’

The sentiment was forcefully articulated in a widely distributed Tumblr post this week in which an unnamed, apparently African American poster wrote: “Dear white protesters, this is NOT about you,” and urged whites to “hand over the bullhorn to a Black person (because your voice doesn’t need a bullhorn to be heard ...).”

And it erupted Tuesday on the steps of Old City Hall in Berkeley, when City Councilman Kriss Worthington, who is white, was repeatedly interrupted as he denounced aggressive police before a crowd of protesters.

“Let a black person talk!” one yelled. “We’ve heard from enough Caucasian men!” yelled another. Worthington handed the mike over to Councilman Jesse Arreguin, who is Latino — and after similar heckling, the megaphone was passed to a black UC Berkeley student who was warmly welcomed.

Black, brown voices

The exchanges during marches have been even sharper at times. One night in Oakland, African Americans staged an alternative demonstration to avoid “march-jacking” by mostly white megaphone-wielders.

“We’re all trying to make sure the white guys with megaphones don’t take over the whole conversation,” said Eileen Santos, 37, a Filipino resident of Berkeley who has been to several marches. “We’re having more brown and black voices, and that’s good.”

Alicia Garza of Oakland, who co-founded the Black Lives Matter online forum in 2013 in response to the killing of Trayvon Martin in Florida, called the tension painful but useful. She is among several black activists who have reached out to Showing Up for Racial Justice — a Caucasian group in support of people of color — to brainstorm ways that white people can participate.

“Having black and brown voices in the forefront makes a lot of sense,” said Garza, 33. “White people are not affected as much as black people by the injustice we are talking about. But white people do have a stake in making sure we have a right to life and a quality of life. This is not a moment for anyone to be on the sidelines.”

'Need to step back’

Amanda Ream of San Francisco, 39, who helped lead a “White Bay Area Residents Civil Disobedience” blockade Wednesday in front of the Oakland federal building, said she and other white activists “have given a lot of thought” to the issue.

“The white people you see out there are driven by their conscience in this moment of great conscience,” Ream said. “But I absolutely think that black people, people of color, need to speak first. This is all unfolding. Anyone who shows up at a protest can grab a bullhorn, but white people need to step back at times and let people of color have their voices.”

The conflict has been most visible with clashes between predominantly young white vandals and black people who try to stop them. Several times in Oakland and Berkeley, African American residents have run out of their houses to yell at white vandals who split away from protests to burn and smash things in the street.

“I cannot stand the spoiled, white privileged kids in masks — and yes, that’s what most of them look like — trying to take over the message by destroying things,” said Moni Law, 54, a housing counselor who lives in Berkeley. She and other black demonstrators have blocked groups from breaking windows at several marches, as have white activists.

'Destroying our city’

Law said she appreciates peaceful intervention by blacks and whites alike, but finds the symbolism of black people preventing destruction particularly powerful.

“A lot of us, 50 to 100 at times, consider ourselves peacekeepers at these protests, and we have mostly been women of color,” she said. “White people — you are our allies, and we appreciate your support, but more importantly your respect.”

Oakland City Councilman Larry Reid, a longtime black-issues leader, said he’s angry at “young white people who are out there destroying our city” with looting that snatches headlines away from the core protest issues.

“There are not many individuals who look like me out protesting and demanding equal justice. Why there has not been a groundswell of African American protesters, I do not know,” he said. “I don’t see the churches getting people out in the streets, and I don’t know why.”

The Rev. B.K. Woodson of Oakland, a leader in the Faith Alliance for a Moral Economy, has an answer for that.

“Within our community, we have a little post-traumatic stress,” he said. “We’ve seen protests come and go, and there is reticence at every level for us, African Americans, to be involved in the street — because we are a target in the street.”

Involving all races

Woodson said he and other clergy have been talking about potential actions for weeks, “but it’s still not clear from the conversation going on all over the country as to what the strategy is.”

Carson and Garza say the strategy is more developed than most people know.

Garza and other activists are pushing for a nationally centralized system for collecting data on police shootings. Carson talks hopefully about convening a community forum that would push for discussions on race relations as suggested by the Congressional Black Caucus.

“The question is how do we change the paradigm, and we will need everyone involved,” he said, “black people, brown people, white people, everyone.”

Chronicle staff writers

Kale Williams, Carolyn Jones

and Evan Sernoffsky contributed

to this report.

Kevin Fagan and Vivian Ho are San Francisco Chronicle staff writers. E-mail: kfagan@sfchronicle.com, vho@sfchronicle.com Twitter: @KevinChron, @VivianHo