Penny Nance slid a form across the table to Donald Trump at his golf club in Bedminster, N.J. Her Christian nonprofit, Concerned Women for America, wanted Trump to pledge in writing that a person’s “gender identity” doesn’t “overrule their sex,” and that if he becomes president again, “all federal agencies will be directed to uphold this fact in every policy and program at home and abroad.” Such a promise would have wide-ranging implications, the form emphasized, affecting schools, prisons, shelters, health care providers, the military and more. But it was an easy sell, Nance recalled of her June 2023 conversation,...