By Shannon Liao, CNN Business

(CNN) -- Axe Body Spray made a bold declaration on Twitter: It supports gay rights and won't be at the controversial Straight Pride Parade set to be held in Boston this August.

The statement on Wednesday began with someone tweeting what they imagined could serve as floats for the Straight Pride Parade. A giant Axe body spray float topped the list.

Axe refuted the association by responding, "we'll be at the parade that matters and this one isn't it."

A second person on Twitter entered the back and forth: "Good to know you don't support straight people...I'm glad, because I think @Axe smells like garbage. #stayoutofpolitics"

Axe then responded: "Gay rights are human rights but go off jill."

The company continued the conversation in replies to other people on Twitter. At one point, the brand Pop-Tarts tweeted "i love you axe." And Axe quipped back, "this is honestly such an honor."

"This is something we've been committed to for years," an Axe spokesman said in a statement to CNN Business. "We stand up for what we believe in and that includes gay rights and rights for the LGBTQ+ community — LOVE is LOVE."

Axe said it will have a presence at the World Pride parade in New York on June 30th. The brand will be part of parent company Unilever's United We Stand float. This year marks the 50th anniversary of the Stonewall riots, which were a turning point for LGBTQ rights.

"Come out and say hello," the company said in the statement.

Axe isn't the only brand challenging perceptions of masculinity. Gillette, owned by Procter & Gamble, and a competitor to Axe, launched its own series of ads in January that tackled social justice issues. The ads explored the #MeToo movement, toxic masculinity, sexual harassment, racism, and transgender rights.

In a Perspectives article for CNN Business, P&G chief brand officer Marc Pritchard wrote, "Gillette has shaped perceptions of masculinity for more than 100 years — including the iconic line 'The Best A Man Can Get' — so it was time to express a more modern, positive view of what it means to be the best in today's world."

Lindsey Roeschke, director and analyst at Gartner, said that Axe and Gillette are aiming at men of different ages — Axe aligning with Gen Z boys, while Gillette is asking older men to take responsibility for the next generation. But they have the same goal.

"What Gillette and Axe are doing is responding to a consumer desire for brands to do more than just sell stuff," Roeschke said.

The other brands named in the Straight Pride Parade float tweet — Doritos, Mountain Dew, and Twinkie — didn't immediately respond to CNN Business' requests for comment.

Many companies have come out in support of gay rights in recent years. Often it's in the form of merchandise or charitable donations — it's rare for a company to be outspoken on social media.

Apple's CEO Tim Cook says he is proud to be gay. Apple has come out with a rainbow flag face for the Apple Watch and matching rainbow band.

Target sells a wardrobe full of pride merchandise every year, and this year it's also donating $100,000 to GLSEN, an organization that aims to end discrimination and harassment of queer students K-12. And Disney is selling rainbow products, including Mickey Mouse ears. 10% of the proceeds go toward GLSEN.

-- CNN Business' Danielle Wiener-Bronner contributed to this report.