“No, I’m not going to the White House,” Ms. Rapinoe said, repeating herself after initially using a profanity to express the same sentiment. “We’re not going to be invited.”

In 2015, Ms. Rapinoe and the United States team won the World Cup in Canada, and the entire team visited the White House for a ceremony with President Barack Obama.

On Wednesday, in his tweet stream, Mr. Trump said that he would invite the team to the White House, “win or lose.” U.S. Soccer said it would have no comment on Ms. Rapinoe’s remarks.

A twin and one of six siblings, she grew up in Redding, Calif., about 200 miles north of San Francisco, and she still speaks with a casual Californian lilt. She came out to her family and close friends in her first year at the University of Portland. She came out publicly a year after the 2011 World Cup, where she had cemented her status as one of the most dynamic players in the country. She had the 35-yard assist on Abby Wambach’s game-tying goal in the waning moments of a quarterfinal against Brazil, one of the biggest goals in U.S. soccer history.

She also became one of the most popular players — among fans around the world and her own teammates — thanks in part to her irreverent sense of humor and a porous filter for her innermost thoughts.

Ms. Rapinoe’s awakening to politics came gradually, later in her career.

On Sept. 4, 2016, while playing for the Seattle Reign in a National Women’s Soccer League game in Chicago, she dropped down to one knee during the playing of the national anthem, becoming the first white athlete and first woman to take part in the protest movement started by Mr. Kaepernick.

The decision launched her into a rapidly boiling national conversation over athletes and activism, earning her months of vitriol from critics along with outpourings of support.