In the center of Capitol Hill, there are two elementary school campuses, Peabody and Watkins, with an unusual setup. Peabody serves the cluster’s prekindergartners and kindergartners. Watkins, about a mile to the south, takes the first- through fifth-graders. The campuses share a principal.

It can be a headache for parents, some of whom shuffle siblings across the two campuses — which have the same start times — before fighting rush hour to get to work. There used to be a city bus to ferry students between the two schools, but it closed about four years ago.

Then, in 2016, a temporary inconvenience bred a permanent solution. Renovations at Watkins forced students to be relocated to a nearby middle school. So the District offered shuttle service to ferry students back and forth.

It should have ended when students returned to their modernized campuses the next year, but the families using the service — mostly the white, more affluent families on the campuses — fought to keep it. They’ve had it ever since, allowing parents to drop off their children at whichever campus is more convenient.

The future of the shuttles is always uncertain. Every year, the mayor proposes to slash the funding, about $260,000 for the most recent school year. Chancellor Lewis D. Ferebee has called it “not equitable.” And every year, the families successfully lobby their D.C. Council members to restore the funding.

This ritual dance continued this year, with the parents organizing a petition to council members. But the push arrived as protesters across the country demanded racial equity and justice, prompting parents to question whether they should still lobby for their shuttle money.

The issue spilled into the parent-teacher organization’s email group and forced reckonings of privilege within the mostly liberal Capitol Hill school community: In a city with drastic wealth and academic gaps, do these families really need the extra funding? Aren’t there low-income students in the city, parents asked, who need it more?

As one Peabody parent pointed out in the email group, it amounts to more than $1,500 in city funds for each child who uses the shuttle. “I’m thinking more these days about what costs we can bear and what creative choices we can make,” another parent wrote.

Last week, a group of parents organized a counter petition calling on the city to not fund the shuttle, saying that the money could be used more “wisely” on efforts to close the achievement gap or digital divide. Sixty-two people have signed it.

The Capitol Hill Cluster, which also includes Stuart-Hobson Middle, was established decades ago to create more racially and socioeconomically diverse schools in the neighborhood. But as the surrounding neighborhood gentrifies, and more upper-income families opt into the public schools, the campuses become whiter and wealthier.

Today, about 61 percent of Peabody’s student body, and 26 percent at Watkins, are white, compared with 11 percent of public school students citywide.

And the vast majority of students who ride the shuttle are white, according to the school’s principal. Many low-income black students who attend the schools don’t live within the boundaries; they opt in through the District’s school lottery. To them, the extra mile makes less of a difference.

Asheley McBride lives outside Capitol Hill, in the Marshall Heights neighborhood of Southeast Washington. She takes a Metro train and city bus to get her son to and from Watkins each day. She read the conversation as it unfolded in the email group and said parents should dig deeper into the question of equity at Watkins, pointing to city data showing that black children at the school are more likely to be suspended than white children.

“Parents who are low-income, who are destitute, make their way to school,” McBride said. “I didn’t understand what the big deal was.”

Laura Tsaggaris, who has a child at each school, lives closer to Watkins. So she drops her kids off at Watkins and lets the shuttle do the rest. She would be open to losing the shuttle, she said, if she understood where the money would go instead.

“In the backdrop of what is going on, we all need to be doing a little more than we have been doing to achieve this equity,” said Tsaggaris, who is white. “Maybe these little decisions are part of it.”

Principal Elena Bell usually sits out the shuttle dance, talking about it only in small settings when parents ask. But this year, as the debate raged in the email group, she spoke up. The shuttles has persisted, she wrote in the email group, because families had the “social capital and influence to make it so.”

“Sometimes, living out the values of equity means you give up something for a greater cause to others who may need it more than you do,” Bell wrote. “Equity is NOT receiving an inequitable resource and doing something nice for ‘families in need’ on the side.”

She said she has come under fire in the past for talking about race and the achievement gap at the school and was “proud” that parents initiated this conversation.

“I’ve been in a difficult space because as principal, you want to advocate for the community,” Bell, who is black, said in an interview. “But how do you do that when what you are advocating for goes against what you fundamentally believe?”

But the conversation may be as far as it goes. The parent-teacher organization, whose top leadership is mostly white, is still backing the shuttle, saying parents should push for the shuttle while also advocating for safe transportation options for all students. The group’s petition also calls for the city to fund transportation for homeless students living in hotels on New York Avenue, which became a flash point last year before the city offered a long-term shuttle for the families.

Zach Lowe, the PTO’s communications chair, said equity and inclusion are integral to the group’s mission. The group is working to ensure black and low-income parents get more involved in the group, he said. The PTO recently sent resources for families to talk to their children about the protests and shared links to protests in the area. And this year, Lowe said, the PTO established a permanent diversity, equity and inclusion position.

If the funding doesn’t come through, Lowe said, he would be open to alternatives, including staggering bell times so families with children at both campuses can more easily get them there on time. Some parents have suggested raising the money themselves, but the school system won’t let them, for liability reasons.

“This isn’t a zero-sum game,” another father said. “We can advocate for the shuttle at our school and for opportunities to help other communities.”

The D.C. Council member whose ward includes Capitol Hill, Charles Allen (D-Ward 6), has said he is in favor of funding the shuttle again, though it’s unclear exactly where the money would come from. It is clear, though, where most shuttle-using parents stand. The petition is still being circulated. In all, more than 150 parents have signed it — roughly the same number who supported the effort last year.

This article has been updated to reflect that some parents started a petition last week after publication calling on the city not to fund the shuttle.