The move fulfills a campaign promise by President Biden, who has raised concerns that without documented proof of their self-identified gender, transgender and nonbinary people risk being denied employment, housing and other benefits, including the right to vote. It also responds to a lawsuit that required the State Department last year to review its earlier denial of a passport applicant who wanted their gender marked with an X. “These changes continue the long-term trend that liberalizes policies governing gender marker changes on identity documents,” said Jami Taylor, a political science professor at the University of Toledo and an expert on L.G.B.T. politics.