Education officials said the decision was the first of its kind on the rights of transgender students, which are emerging as a new cultural battleground in public schools across the country. In previous cases, federal officials had been able to reach settlements giving access to transgender students in similar situations. But in this instance, the school district in Palatine, Ill., has not yet come to an agreement, prompting the federal government to threaten sanctions. The district, northwest of Chicago, has indicated a willingness to fight for its policy in court.