The San Jose State University women’s volleyball team is trying to make the N.C.A.A. tournament for the first time in 23 years. But first, it must find schools willing to play against it.

The University of Nevada, Reno, became the fifth school this season to decline to compete against San Jose State when it pulled out of a game scheduled for last Saturday in response to reports that a player on San Jose’s team is a transgender woman. The others that have decided not to play the team are Southern Utah University, Boise State University, the University of Wyoming and Utah State University.

“We refuse to participate in any match that advances injustice against student athletes,” Nevada’s team posted on social media, referring to what it views as an unfair advantage transgender women have in competition.

The resulting forfeits have pushed the San Jose State Spartans into the middle of the ongoing debate over whether transgender athletes, and particularly transgender women, should be allowed to participate on the team that aligns with their gender identity. That has been a prominent issue in Republican-controlled legislatures in recent years and one that has intensified as a talking point among Republicans in the final days of the presidential campaign.

The refusals to play, along with hateful online messages directed toward the team, have taken a toll on every member of the Spartans, said Todd Kress, the team’s head coach.

“It frankly has been heartbreaking to watch for our student athletes,” he said to reporters after the team lost a match this month. Mr. Kress was unavailable to be interviewed for this article.