This was the same point that Todd Gazda, who at the time was a Massachusetts superintendent, made during a tense school board meeting that took place before he and his district were sued by Mr. Foote, the father of the 11-year-old who said he had learned about his child’s new gender identity from a teacher, who was later fired.

“For many of our students, school is their only safe place,” Mr. Gazda said during that meeting, “and that safety evaporates when they leave the confines of our buildings.” Concerns over parental rights, he added, are in fact thinly veiled “intolerance and prejudice against L.G.B.T.Q. individuals.”

Judges have dismissed many of the lawsuits. In December, a federal judge threw out Mr. Foote’s case, writing that affirming a student’s gender identity was not necessarily a medical intervention or even evidence of social transition, but “simply accords the person the basic level of respect expected in a civil society generally.”

However, the judge acknowledged that “it is disconcerting” that school administrators might “actively hide information from parents about something of importance regarding their child.”

In January, Mr. Foote filed an appeal.

The son of Mrs. Bradshaw, the mother in Southern California, said he has empathy for parents who find it hard to accept that their children are transgender. But he also expressed frustration.

“When parents say they need time or patience it can feel kind of like an excuse for them to keep misgendering you,” he said. “It feels like they are grieving for someone who is not dead, and it makes you feel like you’re not good enough.”

His mother reiterated that she loves her child no matter his gender, but voiced her own frustrations.

“The school is telling me that I have to jump on the bandwagon and be completely supportive,” Mrs. Bradshaw said. “There is only so much and so far that I’m willing to go right now and I would hope that, as a parent, that would be my decision.”

Susan C. Beachy contributed research.