The legal assault on trans rights is being waged on both sides of the Atlantic. This week, Hungary’s Parliament approved a constitutional amendment banning public events by members of L.G.B.T.Q. communities. President Trump sued Maine for allowing trans athletes in schools.

And Britain’s highest court ruled that the legal definition of a woman under the country’s equality legislation is based on biological sex. Trans women, the court said in a headline-making 88-page document, do not meet that legal definition.

The justices said their ruling was based on the precise language of the particular law and not “a triumph of one or more groups in our society at the expense of another,” and that trans people were protected against discrimination under another part of the equality law. But anti-trans groups still claimed an immediate victory, and trans-rights activists decried what they said will have harmful effects on trans people.

The political and legal moves in the United States, Britain and Hungary underscore the power of an issue that animates right-wing movements. They also highlight the stakes for trans people in countries across the world as governments grapple with how to adjudicate competing demands for rights and restrictions.

“Trans communities are devastated by today’s ruling,” said Helen Belcher, the chair of TransActual, a British group that campaigns on behalf of trans people. “Irrespective of the small print, the intent seems clear: to exclude trans people wholesale from participating in UK society. Today, we are feeling very excluded.”

Susan Smith, the co-director of For Women Scotland, the group that brought the legal case, praised the decision, saying that “it’s just about saying that there are differences, and biology is one of those differences.”