At a Coney Island park this summer, children in a basketball summer camp wore blue-and-white uniforms bearing the logo of “The Coney,” a proposed casino project in the neighborhood and the camp’s sponsor.

A few months earlier on Long Island, where Las Vegas Sands is pitching a casino, children from local soccer teams were invited to a Sands-sponsored training session featuring the superstars David Beckham and Carli Lloyd.

In the escalating race to be one of the first to open a casino in the New York City area, developers are rushing to win local support after state regulators said projects needed to be “embraced by the community.” A casino logo emblazoned across youth sports jerseys is just one example of the lengths to which gambling operators have gone to woo those communities and secure a coveted license.

But their sponsorship of these recent children’s events has proved to be as divisive as the prospect of the casinos themselves.

Some parents have argued in outraged Facebook posts that their children are being used as unknowing tools to promote gambling, while other parents expressed gratitude for the opportunities that funding has provided.

Many states, including New York, prohibit casino operators from depicting or targeting minors in their advertising. But, lawyers say, the sponsoring of children’s sporting events by gambling companies often falls into a gray area that states are still seeking to regulate.

New York’s gambling regulators this year proposed a rule, which is still pending, that would prevent the marketing of sports betting to minors — including logos on clothing that are “intended primarily” for people under 21.

The New York City area has never had a full-scale casino — until the State Legislature last year approved up to three new casino licenses for the region. It will most likely be several months before the winning bids are announced, and at least 11 contenders are expected to compete.

In March, Megan and Rich Corrao got a message from their daughter’s soccer coach about a special training clinic at an athletic complex in Nassau County on Long Island.

The Corraos’ 12-year-old daughter was thrilled. Their 9-year-old son tagged along. The flier they had received made no mention of a casino; nor had the message from the coach, Mr. Corrao said.

When Ms. Corrao arrived with her children, she discovered that the event was sponsored by the casino operator Las Vegas Sands. She and her husband were enraged.

“Don’t use our kids as pawns in your effort to dump something in our community that a lot of people really don’t want,” Mr. Corrao said. “It’s not appreciated. It’s not right. They’re not selling bubble gum.”

Ron Reese, a spokesman for Las Vegas Sands, said the company routinely supported children’s education and activities in the communities where it operates. It “adopted” an elementary school next to the casino it used to own in Bethlehem, Pa., and funds a charter school in Las Vegas. And at the March soccer event, the children wore their own team jerseys, and there was limited Las Vegas Sands signage, he said.

“We’ll continue to invest in youth organizations because they’re important parts of the communities in which we operate,” Mr. Reese said.

Anita Means was initially happy when her 15-year-old grandson joined a free basketball clinic this summer hosted by a group called Brooklyn USA Basketball at Coney Island’s Kaiser Park.

Then she learned that the clinic was funded by the Coney Island casino bid, a partnership between the real estate developer Thor Equities, Saratoga Casino Holdings, the Chickasaw Nation and Legends, a hospitality company.

Surrounding the basketball courts were banners with the name of the proposed casino, The Coney. Children played in shirts bearing the same logo.

Ms. Means, a lifelong Coney Island resident, demanded that her grandson stop attending the clinic.

“When I said to him, ‘Well, who you playing for?’ he didn’t say the casino,” Ms. Means said. “He didn’t know it involved a casino.”

Event organizers said the children were not required to wear the branded shirts, although the social media pages for Brooklyn USA Basketball seemed to exclusively show photos and videos of children who did.

Lakeisha Bowers, whose 12-year-old son is playing in the clinic, found out about the casino sponsorship only when she showed up to Kaiser Park and recognized the logo. She was furious that the organizers had not notified parents ahead of time.

Ms. Bowers, who is a member of the local community board in Coney Island, which opposes the casino, stopped her son from posing in a group photo with the casino-branded shirt but allowed him to stay in the program because he loved basketball.

She said the clinic’s free backpacks and water bottles were difficult to turn down in a community where there are limited summer activities for children. She now sees residents all over the neighborhood wearing the casino-branded shirts.

“They’re using our children to promote a casino,” she said. “If all the kids’ parents are aware of that and they’re still OK with it, then it’s fine by me. But let’s not make it a secret.”

The founder of Brooklyn USA Basketball, Thomas Sicignano, said his group had hosted 10-week clinics every year for the last 12 years. Because of the casino’s sponsorship, he said, this was the first year that the clinic could afford uniforms for every child, as well as a full staff to help coach and organize the program.

A consultant for the casino project, Domenic Recchia, said the group was figuring out how to expand its children’s programming in the fall, noting that the shirts do not say “casino.”

Since the basketball clinic started in July, critics of the Coney Island casino bid have seized on the issue to stir up opposition among local residents, posting outraged messages on Facebook about children in casino-branded clothing that have sparked heated exchanges between pro- and anti-casino partisans.

Robert Cornegy Jr., a former New York City councilman and professional basketball player who is also working as a consultant for the casino project, said that the casino bid was responding to the community’s requests for more youth programming.

“Everybody said, ‘We’re not listening to anybody about anything unless you’re willing to leverage whatever resources that you have to benefit our children,’” Mr. Cornegy said. “And any community is going to say the same thing.”

Mr. Cornegy added that it was routine for children to wear the names of league sponsors on their jerseys, even if those sponsors promote adult activities.

“I’ve had the names of everything from liquor stores to churches on the shirts I’ve played in,” he said.

On a recent Saturday afternoon, some parents at the basketball clinic said they did not know what The Coney was. Others did know, but said they welcomed the sponsorship because it gave their children an opportunity they might not otherwise have.

Paul Jarrett, whose 9-year-old son was playing, said the casino’s involvement was “not an issue” for him.

“He has a real interest, and we want to cultivate it,” Mr. Jarrett said.

Sadef Ali Kully contributed reporting.