Before her decision to step down, Sturgeon faced a battle over transgender rights.

A battle over her support for transgender rights is not, by Nicola Sturgeon’s account, the reason she is quitting as Scotland’s first minister. But the issue has dogged her in recent weeks, precipitating a clash with the British government and ensnaring her in a messy episode involving a convicted rapist who was held in a women’s prison.

Ms. Sturgeon’s problems began in December when the Scottish Parliament passed legislation that would allow transgender people to have the gender with which they identify legally recognized and to get a new birth certificate without a medical diagnosis. Britain’s government swiftly rejected the law, saying that it conflicted with equality laws that apply across Britain, including Scotland.

That prompted a crisis in Britain’s power-sharing system, known as devolution, with Ms. Sturgeon calling it a “a full-frontal attack on our democratically elected Scottish Parliament and its ability to make its own decisions.”

For Ms. Sturgeon, the transgender legislation is part of her declared commitment to protect minority groups. But while the law was supported in Parliament, it has divided the broader Scottish population and become a cudgel in the culture wars.

It has also become conflated with the case of Isla Bryson, a transgender woman who was convicted of raping two women before her transition. She was initially placed in a women’s prison while awaiting sentencing, a decision that prompted an outcry by critics who said it jeopardized the safety of other inmates.

Ms. Sturgeon later announced that Ms. Bryson had been moved to a men’s prison. But the handling of the case exposed Ms. Sturgeon to sharp criticism and put her in an awkward position when she was quizzed repeatedly at a news conference about whether she regarded Ms. Bryson as a woman.

“She regards herself as a woman,” a visibly frustrated Ms. Sturgeon replied. “I regard the individual as a rapist.”

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