A group of protesters gathered outside one of Netflix Inc.’s Los Angeles offices Wednesday to express their anger over the streaming giant’s Dave Chappelle comedy special, as some employees released demands for management and staged a walkout.

In the special, “The Closer,” Mr. Chappelle made jokes and remarks regarding gender that many in the transgender community, including some Netflix staffers, found offensive. The company has defended the special, citing reasons including the company’s commitment to artistic freedom.

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A group of protesters gathered outside one of Netflix Inc.’s Los Angeles offices Wednesday to express their anger over the streaming giant’s Dave Chappelle comedy special, as some employees released demands for management and staged a walkout.

In the special, “The Closer,” Mr. Chappelle made jokes and remarks regarding gender that many in the transgender community, including some Netflix staffers, found offensive. The company has defended the special, citing reasons including the company’s commitment to artistic freedom.

Carrying signs that read “Transphobia Isn’t Funny” and “Trans Lives Matter,” protesters demanded that Netflix offer more inclusive programming and be more sensitive to the effect its content can have on certain communities and society as a whole.

Some Netflix employees attended the event, but didn’t speak. Supporters of the comedian also showed up and tried to disrupt the proceedings.

The event was organized by Ashlee Preston, a trans activist. “If your satire is punching down you are being a bully,” Ashlee Preston said. “I’m tired of companies like Netflix making money off of trauma to my community.”

The extent of the walkout wasn’t clear. Many employees are working remotely.

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In a list of demands sent to Netflix management, a group of transgender employees called on the company to create a new fund to develop trans and nonbinary talent, recruit more trans people into leadership roles, and add a disclaimer “before transphobic titles that specifically flag transphobic language, misogyny, homophobia, hate speech, etc. as required.”

The employees wrote that those changes and others were necessary “to avoid future instances of platforming transphobia and hate speech, and to account for the harm we have caused and will continue to cause until the below measures are put in place.”

Netflix said in a statement: “We value our trans colleagues and allies, and understand the deep hurt that’s been caused. We respect the decision of any employee who chooses to walk out, and recognize we have much more work to do both within Netflix and in our content.”

A Netflix spokeswoman declined to comment on the specific demands.

In an interview Tuesday, Netflix co-chief executive Ted Sarandos said he “screwed up” in his communications with staff over the controversy. He had cited the popularity of Mr. Chappelle’s special and had said the company didn’t believe programming can spur real-world harm.

“I should have recognized the fact that a group of our employees was really hurting,” he said in the interview.

Write to Joe Flint at joe.flint@wsj.com