Ms. Hill, who campaigned to make history as the first openly bisexual congresswoman from California, unseated a Republican, Steve Knight, in the so-called blue wave that carried Democrats to power in the House in 2018. She is a favorite of Ms. Pelosi, who named her vice chairwoman of the House Oversight and Reform Committee, an unusually high-ranking position for a freshman on a panel that is playing a crucial role in the impeachment inquiry into President Trump.

Ms. Hill represents parts of the Santa Clarita and Antelope Valleys, the most conservative district in Los Angeles County, and is expected to have a tough re-election race there. Since the RedState report, her Republican critics have been circulating the nude photo on Twitter, which has taken the posts down for violating the platform’s rules against sharing explicit images of someone without their consent.

“She’s a victim of revenge porn, which is a form of domestic violence and psychological abuse,” said Kat Walker, a gun control activist and Hill supporter, who said she had spent the past several days reporting Twitter users who posted the photo. “We worked very hard for her. I already know I’m going to have to work very hard for her again, scandal or no scandal.”

The report involving Ms. Hill — and the House leadership’s muted reaction to it — comes in the context of the #MeToo movement, amid heightened sensitivity about the conduct of men in positions of power, including members of Congress. It raises questions about whether there is a double standard for men and women who engage in intimate relationships in the workplace.

RedState also published what it characterized as text messages between Ms. Hill and the campaign aide, who was not identified, that suggested Ms. Hill was breaking off their apparently consensual relationship so she could focus on her duties in Washington. If that is true, experts in workplace law said, it might be inappropriate but not illegal.

“Clearly there is an inherent power differential between Congresswoman Hill and a young campaign staffer who worked for her, but there’s nothing unlawful about having a relationship with people who work for you as long as it is consensual,” said Debra Katz, a Washington lawyer who represents victims of sexual harassment. “But clearly this shows bad judgment.”

Some male Democrats said privately on Tuesday that if Ms. Hill had been a man, there would have been an immediate uproar that would most likely have ended in a forced resignation. In recent years, several men have resigned from Congress after stories about their sexual conduct, but those resignations often involved allegations of harassment.