In the court of public opinion, with the marriage equality campaign moving toward success, a climate of acceptance was growing and extending from sexuality to gender identity. “Suddenly people liked us,” Ms. Keisling said.

It helped that the movement was growing younger and more diverse. In 2013, a website called “We Happy Trans” published its inaugural “Trans 100” list, which included veterans like Ms. Frye but also new stars, like Laverne Cox, 31, a black transgender actress featured in the Netflix television series “Orange Is the New Black.”

To be sure, as Ms. Cox often emphasizes, life remains excruciatingly hard for many transgender people who continue to face discrimination, hostility and violence in many families, neighborhoods, schools, workplaces, police precincts and prisons. Rates of attempted suicide, H.I.V. infection, unemployment, poverty and homelessness are exceptionally high, especially for transgender women of color.

Still, seen through Ms. Frye’s long lens, the progress is undeniable.

After more than four decades with her wife — “and even though I had hair on my face when Trish and I married” — Ms. Frye exhaled deeply when the Supreme Court legalized same-sex marriage, she said. “It’s always been in the back of our minds all these years, that somebody could challenge us,” she said.

In her private law practice, which she maintains alongside the part-time judgeship, she exclusively represents transgender people now, and is taking ever more children through the process of changing their names and gender markers. “Their parents call me,” she said. “Who’d have imagined?”

She does not miss the intensity of the struggle, she said. “I’ve enjoyed my 60s. I haven’t had to fight.”

Though she watches the movement’s building momentum with occasional incredulity — “Even the military!” she exclaimed, referring to the announcement in July that the Pentagon plans to lift its ban on service by openly transgender people — she has been waiting with impatience for society to catch up with her.

“I keep wondering what took her so long,” she said about Caitlyn Jenner’s introduction to the world. “She could have done a lot of good.”

New Normal One night this summer, in a basement courtroom at the Houston Municipal Courthouse, Ms. Frye emerged from chambers, zipping up her robe over her khakis and telling a smattering of defendants, “Don’t get up.”

Under a low ceiling, she settled on the bench, between the American and the Lone Star flags, in front of a framed photograph of Mayor Parker, who fought back tears at Ms. Frye’s swearing-in in 2010.

Chatting with the clerks, the judge questioned the air-conditioning — “Is it hotter than a firecracker in here, or is it just me?” — and described how she lost 70 pounds over the last few years, changing her diet and working out daily in her fitness room (at the same modest house that was egged decades earlier).

For the next several hours, she dealt amiably and efficiently with a sleepy stream of mostly sheepish traffic violators.

“Hawkins,” she said, summoning a jaunty man wearing earrings. “How are you?”

“I’m doing pretty well, judge. Yourself?” Mr. Hawkins replied.

“I’m terrific,” Ms. Frye replied. “You were supposed to bring $279 plus your license plus proof of insurance.”

Mr. Hawkins said he had run into a “small problem.” He was unable to get a new license because he owed $2,200 in surcharges to the city.

“I hope you’re not driving now,” Judge Frye said, holding up her hand. “Don’t tell me. Don’t tell me.”

She gave him a 60-day extension, and he thanked her, saying he had never gotten one that long before.

“Well, you ain’t getting any more,” she said.

If prosaic authority is the summit of normalcy, then Ms. Frye, who once harangued a federal official for treating her like “a freak,” has reached it.

“Whatever normal means,” she added.