Student Mars Proppe, who identifies as nonbinary (neither male nor female) hoped one day to have a passport marked “X” for gender. But when Iceland’s government made that choice possible a year ago, Proppe had second thoughts.

While more than a dozen countries have introduced gender-neutral travel documents, some nonbinary and transgender people are reluctant to use them because they fear discrimination or bureaucratic hurdles when travelling abroad.

“I have yet to go and get my master’s degree and hopefully travel through the world, and that’s not something I think I can do ... if I have an ‘X’ on my passport. At least, I can’t do it really safely,” said Proppe, 23, who studies astrophysics...