A bitter custody battle in Dallas that centers on the gender identity of a 7-year-old child provoked an outcry among conservatives this month.

The child’s mother, Anne Georgulas, had honored what she said was the child’s preference to live as a girl and sought to compel the father, Jeffrey Younger, to do the same, according to court documents. But Mr. Younger insisted that the child is a boy and said that Ms. Georgulas was manipulating the child’s identity.

The case attracted major interest after Mr. Younger created an extensive website, posting photos and videos of his children and sitting for interviews with conservative podcasts and news outlets . He raised tens of thousands of dollars in donations, saying that he was fighting forced and irreversible medical procedures, though experts who treat transgender youths disputed that characterization.

In a ruling on Thursday, Judge Kim Cooks in the 255th District Court in Dallas said that the parents should have joint custody and that the state could not require Mr. Younger to treat the child as a girl. She also forbade either parent from speaking to the news media and ordered Mr. Younger to shut down his site. (It appeared to have been taken down on Friday.)