In a memo, teams at the consulate in Rio de Janeiro and the embassy in Brasília suggested that in light of Brazil’s increasing political polarization under Mr. Bolsonaro, their actions would “be an opportunity to show support for not only the L.G.B.T. community but minority rights as well,” while showcasing “pride and confidence in our own diversity and strength as a society.”

The State Department’s curt rejection left gay personnel and their backers reeling. In conversations this past week, American diplomats who are gay described a prevailing mood of fear and angst. None would speak on the record for fear of retaliation.

Robyn McCutcheon, a foreign service officer who in 2011 became the first transgender American diplomat to transition on the job, expressed disappointment in a recent blog post about the department’s decision not to issue the standard yearly cable encouraging embassies to mark gay pride or a day against homophobia that is observed every May 17.

“Day by day, a death by a thousand cuts, our rights as lgbt+ Americans are being eroded with the removal of a guidance here, the rewriting of a policy there, or just the quiet disappearance of a website,” she wrote.

Officials at the State Department did not respond to questions about the flag policy or say whether the advancement of gay and transgender rights continues to be a foreign policy priority. And while they declined to shed light on the intent of the new commission, Secretary of State Mike Pompeo recently told reporters it would help him decide how to think about human rights in diplomacy.

“How do we make sure that we have a solid definition of human rights upon which to tell all our diplomats around the world how to engage on those important issues?” he asked.