Posters that read “Silence = Death” from the early years of the AIDS epidemic. A pair of sneakers signed by Ellen DeGeneres, who famously announced, “Yep, I’m Gay” on the cover of Time. A gavel that repealed the “Don’t Ask, Don’t Tell” policy.

For more than five decades, the Stonewall National Museum, Archives and Library in Fort Lauderdale, Fla., has chronicled the L.G.B.T.Q. community by collecting and sharing its history.

But the museum, one of the country’s oldest such institutions, is facing a hostile political environment and a financial crisis that may force it to find another home.

The organization has been hampered by recent budget shortfalls that Robert Kesten, its president, attributed to President Trump’s ongoing crackdown on diversity programs and anti-L.G.B.T.Q. policies led by Gov. Ron DeSantis of Florida. Corporations have also pulled back on sponsorships for national L.G.B.T.Q. groups like the Stonewall museum, which began as a small collection in 1973.

Named for the 1969 uprising in New York City, when a police raid at a Greenwich Village gay bar called the Stonewall Inn set off the modern gay rights movement, the 4,500-square-foot space houses a collection of more than 30,000 books (including some banned at certain public schools) along with DVDs, historical documents and artifacts that reflect the ongoing fight for equality.

Organization officials say they are doing their best to keep the institution’s doors open to preserve the repository for future generations, but it has been challenging.

“In federal and state funds, we are down 100 percent,” Mr. Kesten said about the cuts to its $1 million annual budget.

Among the funding that has been cut off, he said, are grants of $10,000 to $25,000 that the organization received annually from both the National Endowment for the Humanities and the federal Education Department; a $50,000 grant from the Florida State Department’s Division of Arts and Culture; and annual grants of $25,000 to $50,000 from Florida Humanities, a nonprofit state affiliate of the N.E.H.

In addition, Mr. Kesten estimated that around $100,000 in corporate sponsorship funding had dried up.

“What has been worse for us is the demand of corporations to eliminate their D.E.I. efforts,” Mr. Kesten said, referring to diversity, equity and inclusion programs. “We received multiple awards from various corporations — a few were considering, or had agreed, to join our board. Those contacts no longer return calls or texts; they no longer sponsor events. They have backed off joining the board.”

The N.E.A., which has been withdrawing grants to arts groups nationwide this year, said in a recent update it to its grant guidelines that was shared with Stonewall that “funding priority” would be given to projects that “celebrate and honor the 250th anniversary of the signing of the Declaration of Independence.”

The White House and the governor’s office did not comment on the museum’s funding shortfalls.

The history of the L.G.B.T.Q. rights movement is one of immense challenges, and museum officials said they might have the best resources to guide their survival — their own archives.

“Based on our archives and library, we have blueprints on how to fight back, and to survive with less, and how to keep our community alive and rebuild as we have for generations,” Mr. Kesten said.

Donations from individuals, including from the estates of deceased supporters, have helped Stonewall offset some of the losses. “With our cautious spending, we are holding our own but cautious not to take on more than we can,” Mr. Kesten said, adding that he has not filled three vacancies at the museum.

Here are some of the more popular items in the archive.

A Village People Gold Record

Stonewall is home to a framed gold record issued to the disco group Village People for selling more than 500,000 copies of their 1978 album “Macho Man.” The group was named after characters in gay clubs in Manhattan’s West Village.

Randy Jones, the group’s cowboy, donated the gold record to Stonewall in 2015.

Created in 1977, Village People found mainstream success with campy songs like “Y.M.C.A.” In the song’s music video, members are dressed as American masculine archetypes, such as a cowboy, construction worker, police officer, soldier and Native American.

Despite the song’s longtime association with the gay community, President Trump has embraced it and even joined Village People onstage in January for a singalong.

The ‘Don’t Ask, Don’t Tell’ Gavel

This was the gavel that Representative Nancy Pelosi, when she was the House speaker, used when the chamber voted in 2010 to repeal the “Don’t Ask, Don’t Tell” policy, which prohibited gays and lesbians from openly serving in the U.S. military.

Enacted by President Bill Clinton in 1993, the policy allowed gays to serve in the military as long as they kept their sexuality a secret.

The foot-long gavel was donated to the archive by former Representative Barney Frank of Massachusetts, a longtime supporter of the L.G.B.T.Q. community.

“Repealing the discriminatory ‘Don’t Ask, Don’t Tell’ policy will honor the service and sacrifice of all who dedicated their lives to protecting the American people,” Ms. Pelosi said on the House floor in 2010.

A Tennis Racket Signed by Martina Navratilova

A red-white-and-blue Bosworth racket signed by one of the most dominant players in tennis history is part of the collection at Stonewall and will be featured in an upcoming display of sports memorabilia from the museum’s collection, Mr. Kesten said.

Martina Navratilova, a Czech-American who played her first Wimbledon as a 16-year-old in 1973, won 18 Grand Slam singles championships. The archive also has her jacket from a Virginia Slims tournament and a signed ball.

Fans of “The Real Housewives of Miami” may have seen Ms. Navratilova, 68, on the Bravo reality TV series because her wife, Julia Lemigova, is a cast member and cameras follow their relationship and expanded family.

Ricky Martin’s Leather Pants

The gay Puerto Rican pop star and actor started his career as a member of the boy band Menudo in the 1980s. As an adult, he became a successful solo artist who catapulted to a meteoric level of fame with his hit song “Livin’ La Vida Loca” in 1999.

In 2010, Mr. Martin shared his private struggles with being gay in the public eye and becoming a father in his memoir, “Me.”

“Before Ricky Martin came out, it was that much more difficult for Latino men to come out and be gay,” Mr. Kesten said.

The Marlin Beach Hotel Sign

The 88-room Marlin Beach Hotel was a popular beach spot for gays in Fort Lauderdale for the second half of the 20th century, and its outdoor sign, which features a muscular man holding up a marlin, is kept at the museum.

The hotel, which was built in 1954, “was among the first large beach hotels that helped the city mature as a tourist resort,” a panel at Stonewall reads.

The archive includes the hotel’s original blueprints as well menus, news clippings and advertisements in national gay magazines, which promoted the hotel as “America’s premier gay resort.” The hotel was torn down in 1992 and is now an open-air mall.

“The shadow cast by these policies,” and the upending of the museum’s funding model, has “increased the level of fear” as the museum tries to stay afloat, Mr. Kesten said.

And yet, he added, “it’s always important to be where you’re not wanted, and to remind people that you exist.”