There is relatively sparse nonpartisan polling on these issues, but a survey from the Public Religion Research Institute last year found that while 82 percent of Americans supported laws that protect L.G.B.T.Q. people from discrimination, they were more uneasy about other questions.
Only 36 percent of Americans surveyed said transgender girls should participate with other girls in high school sports. A Gallup poll last May found that 62 percent of Americans said transgender athletes should be allowed to play only on sports teams that matched their gender assigned at birth, though an earlier Marist Poll survey found far more opposition to a bill barring transgender student athletes from sports teams that reflected their gender identity.
In all that turmoil, Republicans see a political opening.
Lawmakers in states beyond Florida have recently signaled intentions to emulate the state’s new law. Opponents warn that parts of the law may have a chilling effect on teachers and on students of all ages, including some who have relied on schools as a safe place to talk about personal issues.
The debate has turned ugly: Some proponents of the Florida law call its critics “groomers” — a term associated with pernicious decades-old smears suggesting that L.G.B.T.Q. people pose a threat to children.
Several states have also passed restrictions on transition care for minors, and the governor of Texas directed state officials to view medically accepted treatments for transgender youths like puberty blockers and hormones as abuse, a policy that quickly became the subject of litigation. On Friday, Alabama’s governor signed legislation that stops medical professionals from providing care that helps transgender young people in transitioning, among other sweeping restrictions.
Supporters of the bills frame the push on girls’ sports — a subject that has appeared in some Republican campaign ads — as a matter of fairness for female sports competitions and part of a broader set of parental concerns, even as Democrats and some Republicans question what real-world problems these measures are intended to solve.
“I hope the left doesn’t understand how big of a deal it is,” said Tony Perkins, the head of the Family Research Council. “They’ll never know what hit them.”