majority of transgender students report feeling unsafe at school because of bullying and harassment.

“What we have is a speculative fear of something that hasn’t materialized,” Mr. Strangio, who is a transgender man, added. “They’re acting like LeBron James is going to put on a wig and play basketball with fourth graders. And not one LeBron James, 100. In reality, you’re talking about little kids who just want to play rec sports. They just want to get through life.”

packaging transgender-specific restrictions. Borrowing a page from the anti-abortion movement, which was led by men for much of its early period, they have begun featuring women as public advocates.

“Fairness in Women’s Sports Act” into law last week, the leading proponents were the attorney general, Leslie Rutledge, who is a candidate for governor, and the Arkansas Republican Women’s Caucus. The bill will prohibit transgender participation on female teams from kindergarten through college.

In many instances, lawmakers have worked closely with groups like the Alliance Defending Freedom, a conservative legal organization that has argued several Supreme Court cases on behalf of people claiming discrimination because of their traditional beliefs about marriage and gender roles. Providing messaging, polling and political support are groups like the American Principles Project, Concerned Women for America and the Heritage Foundation.

In the ongoing case in Idaho, opponents of the law argued that it was exclusionary, discriminatory and a violation of the Equal Protection Clause of the Constitution. The Alliance Defending Freedom, which is representing two female college runners who said they had “deflating experiences” after losing to a transgender woman, agreed that the case was about equality, but in the context of creating “a level playing field.”

“When the law ignores the legitimate differences that exist between men and women, it creates chaos,” said Kristen Waggoner, the group’s general counsel. “It also creates enormous unfairness for women and girls in athletics.”

A new study by the Public Religion Research Institute reported that only 7 percent of Americans are “completely against” pro-L.G.B. T.Q. policies. But it is a vocal group intent on showing that it can flex its power in the Republican Party.

When Ms. Noem sent the bill back to the South Dakota Legislature on March 19, despite having said on Twitter that she was “excited to sign this bill very soon,” social conservative organizations went on the attack, taking aim at her apparent presidential ambitions as a potential Achilles’ heel. “It’s no secret that Gov. Noem has national aspirations, so it’s time she hears from a national audience,” the Family Policy Alliance, an affiliate of Focus on the Family, wrote in an email to supporters.

Ms. Noem appeared to be aware of how damaging it could be to have conservatives think she was on the wrong side of the issue.

On Thursday, she and her advisers joined a hastily arranged conference call with members of the Conservative Action Project, which includes leaders of the largest right-wing groups in the country. Ms. Noem expressed concern that if she signed the law, the N.C.A.A. would retaliate against South Dakota, as it did with North Carolina, by refusing to hold tournaments there, according to one person on the call. She has said she will sign the bill only if the provisions that apply to college athletics are taken out.

The activists were respectful but clear, this person said, telling her this was not what they expected from the conservative firebrand they had come to admire so much.

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