Tens of thousands of visitors arrive at Walt Disney World this weekend for an unofficial gathering of gay parkgoers. This year’s Gay Day, as the event is known, comes as Disney navigates political, customer and employee tensions over lesbian, gay, bisexual and transgender issues.

Disney has criticized Florida’s Parental Rights in Education bill, a GOP-led measure that bans classroom instruction on sexual orientation and gender identity through third grade and limits it in later grades. Florida legislators hit back at the company, ending one of its long-held tax breaks.

Some LGBT travelers say they considered boycotting trips to Florida before Disney spoke out against the law, which opponents have called the “Don’t Say Gay” bill. Many have decided to keep their plans this June, reasoning that showing up to the park near Orlando, Fla., would make a bigger statement.

“By boycotting, you’re boycotting a community of people that had no control over what happened in Tallahassee,” says Tom Christ, a producer of One Magical Weekend, one of the related events happening this weekend. He estimates at least 8,000 people would attend his group’s events.

Gay Day, also called Red Shirt Day, has become a fixture at the park, but it isn’t officially sponsored or sanctioned by Disney. Other LGBT-themed events take place the first weekend of June, not all focused on Disney. (Bud Light and Smirnoff are among the sponsors of some off-site events.)

“It is profound for us to be proudly queer in a place that is associated with family and innocence and magic,” says Christopher Hook, a travel agent who specializes in Disney vacations and regularly attends the events.

LGBT travelers have historically worn red shirts to the Magic Kingdom on the first Saturday in June.

Photo: Getty Images

In Orlando, Disney takes a hands-on, hands-off approach to the events on theme-park grounds, organizers say. Gay Day is one of several large events at Disney parks planned by outside groups. The company does sponsor a gay-pride event at its Paris park.

Disney World introduced pride-themed photo backdrops in parks this month, and its stores sell pride-themed merchandise. The company is donating 100% of profits from sales of that merchandise to organizations that support LGBT youth and families, Lisa Becket, a marketing executive, said in a blog post. The company previously donated part of the profits.

LGBT travelers bring big money to Florida and Orlando. State and local tourism offices have marketed themselves as friendly destinations. Visit Orlando, the city’s official tourism association, estimates approximately 2.9 million U.S. LGBT visitors a year contribute more than $2 billion in direct visitor spending.

Photos: How Disney Carved Out Its Own Government in Florida
Hulton Archive/Getty Images

Gay Day has grown from a single-day event at the Magic Kingdom into several days of events across the area during the first weekend in June. Disney isn’t the primary focus for organizers like Gay Days Inc., which hosts pool parties, drag shows and other adult-themed events at a hotel off-site. Others, such as One Magical Weekend, rent out Disney’s Typhoon Lagoon for a Friday night party.

The centerpiece for many travelers is Saturday’s Red Shirt Day, which originated at Disney’s Magic Kingdom in 1991 when a small group of LGBT visitors wore red shirts, as opposed to rainbow-colored attire, to signify their presence and show solidarity.

A Disney-and-LGBT-themed T-shirt design.

Photo: Married With Mickey

“As a cast member, that was one day a year where I felt like I was safe and belonged,” says Chantel Reshae,

who worked at Disney during the initial event and is now director of entertainment for the Gay Days organization.

Disney’s relationship with its LGBT fan base has evolved and deepened over the years. In the early 1980s, same-sex couples were often told they couldn’t dance in the parks, a policy Disney reversed by the end of the decade. The Southern Baptist Convention declared a boycott of Disney in 1997 that lasted eight years, in part because it viewed the park as doing nothing to stop the Gay Days events.

Disney parks have a fervent LGBT following, with social-media influencers crafting personas around their lives as self-described Disney Gays. The company’s movies and shows have in recent years introduced LGBT story lines and characters, from “Eternals” to its coming “Lightyear.” Some employees and fans have called for the company to do more.

Disney’s approach to the Gay Day events has changed, says Eddie Shapiro, producer of Gay Days at Disneyland in California. Previously, he says, park workers passed out white shirts to attendees who mistakenly wore red and gave refunds to customers unhappy that they attended during these events.

Now, the company donates park tickets to the Orlando Youth Alliance, a nonprofit that serves LGBT youth in central Florida, for the first Saturday in June. In Anaheim, the home to California’s Disneyland resort, outfits such as Disney Vacation Club sponsor the Gay Days event, he says.

“I have a long, long history of watching Disney make some mistakes when it comes to this community, understanding those mistakes, learning from them, growing and moving forward,” Mr. Shapiro says.

Beth Parish and her wife are taking their two children from the Chicago area to Disney this week to celebrate Gay Days. Ms. Parish, an attorney and transgender woman, says she isn’t happy about spending money in Florida given the state’s recent legislation.

That the park is open to all customers during Red Shirt Day is important to many travelers. Ms. Parish, 44, says she hopes that her kids, both under 10, will see other LGBT families—and that other park guests can see she is just another parent whose children roll their eyes when she tells them no.

“We’re a normal, boring family,” she says. “I think that’s important.”

Write to Allison Pohle at allison.pohle@wsj.com and Erich Schwartzel at erich.schwartzel@wsj.com