Mr. Young would typically just repost such a story, said a person familiar with his site. Instead, the singer decided to pen his own letter about Spotify. “They can have Rogan or Young. Not both,” the 76-year-old activist artist wrote to both his management and his record label, asking they remove his music immediately.

Two days later, Mr. Young’s label told Spotify to take down his music, and it obliged.

For most of the week after Mr. Young’s ultimatum, it didn’t feel like a crisis at Spotify, said people inside the company.

But gradually, other artists and podcasters followed Mr. Young’s lead. Five days after the singer’s first volley, Spotify executives decided they had to act before the weekend was over and before the problem snowballed.

“We were too slow to respond,” Chief Executive

Daniel Ek

said in an interview. The company had been looking for ways to respond to the open letter before Mr. Young’s demand surfaced, he added. “That’s on me.”

The spat has been a rude wake-up call for Spotify as it seeks to become the world’s largest audio company. Like

Facebook

and YouTube, Spotify started as a tech platform agnostic to what it hosted. But it is now moving toward being a media company that is responsible for what it distributes. The shift means, like it or not, the company is confronting some difficult decisions about content that can spark heated reactions from consumers, employees, artists and podcasters.

Mr. Ek in the interview resisted being pinned down as a publisher. He said it is still debatable whether YouTube and Facebook are tech or media platforms. “I don’t think you can define exactly what Spotify is either,” he said.

This week, Spotify reported it had 406 million monthly active users, up 18% from the year before. Its advertising revenue, largely tied to podcasting, was up 40%.

A representative for Mr. Young declined to comment. Representatives for Mr. Rogan didn’t respond to a request for comment.

Mr. Young didn’t inform his label before posting his Jan. 24 letter. It took several hours before it was widely noticed there or at Spotify, said people familiar with the timeline.

Mr. Young has acted on his principles before, leading to friction with the music industry. In the 2010s, he crusaded for better digital-sound quality and created Pono, his high-resolution music player and download service. He pulled his music from streaming services temporarily in 2015 over sound-quality objections. On his website in recent days, he has described Spotify’s sound as “sh—y degraded and neutered” and encouraged people to leave the service.

The open letter that sparked his action cited a podcast episode in which Mr. Rogan spoke with Dr. Robert Malone, a virologist who worked on research into several mRNA Covid-19 vaccines but who is now critical of the treatments. The signatories accused Mr. Rogan’s podcast of “promoting baseless conspiracy theories.”

Mr. Young echoed this critique in his Jan. 24 letter, which he took down the next day as media outlets began to write about it.

Throughout discussions on Jan. 25, Mr. Young’s management team and label—

Warner Music Group Corp.’s

Warner Records—weighed whether or not to wait for Spotify to respond, said people familiar with the talks, but Mr. Young didn’t waver. Warner is the licenser to Spotify and legally has control over how his music is distributed. It is typical for a record company to take an artist of his stature’s wishes into account. The next day, it officially asked Spotify to remove his music, said people familiar with the request.

As his music was coming down, Mr. Young wrote on his website: “I sincerely hope that other artists and record companies will move off the Spotify platform and stop supporting Spotify’s deadly misinformation about Covid.” He began pointing fans to where his music is still available to stream, including on

Apple Inc.’s

Apple Music,

Amazon.com Inc.’s

Amazon Music and Qobuz, a high-res music streamer.

On the day Mr. Young’s music came down, Spotify issued a written statement, saying: “We want all the world’s music and audio content to be available to Spotify users. With that comes great responsibility in balancing both safety for listeners and freedom for creators.”

Spotify said it had content policies in place and had removed over 20,000 Covid-19-related podcast episodes during the pandemic, adding: “We regret Neil’s decision to remove his music from Spotify, but hope to welcome him back soon.”

On Jan. 27, Spotify’s competitors began welcoming new users in tweets supporting Mr. Young.

Sirius XM Holdings Inc.

revived Mr. Young’s satellite and streaming-radio channel. Record labels were fielding calls from artists and artist managers inquiring about taking their own music down, said industry executives. They began pressuring Spotify to do more, finding frustrating what they perceived to be the company’s lack of a real response.

Mr. Ek offered to meet with Mr. Young several times this past week, said people familiar with the outreach, but the artist didn’t take him up on it. Mr. Young wanted instead to talk with some of the doctors who signed the original letter to learn their thoughts about Spotify’s response, according to people familiar with the artist’s thinking.

Inside Spotify, frustration among some employees boiled over after Mr. Young took action, said people inside the company. Many staffers already had been concerned about the company’s silence in response to the open letter.

“The Neil Young letter was one of those things where this isn’t a big deal until it becomes a big deal,” said one Spotify executive. “Part of Spotify’s proposition is get all your audio in one place—if you have big artists who aren’t available, if Drake or Taylor Swift pulls off, it’s a real problem for the proposition.”

Spotify tries to foster an egalitarian culture and encourages employees to openly debate topics as diverse as app updates and the snacks available in the office. Since Mr. Rogan’s addition to Spotify in September 2020, some employees have used message boards to express their concerns about his show, said people inside the company.

On Jan. 28, singer-songwriter Joni Mitchell, who is also signed to Warner Music Group and shares a manager with Mr. Young, joined him in quitting Spotify. “Irresponsible people are spreading lies that are costing people their lives,” she wrote on her website. Other peers of Mr. Young later issued similar statements, including former bandmates David Crosby, Stephen Stills and Graham Nash.

Neo-soul singer India Arie said she too wanted to remove her music and podcast, based in part on Mr. Rogan’s discussions around race. Podcasters who pulled their shows included professor Brené Brown, who tweeted on Jan. 29 that she wouldn’t produce more for the service until further notice.

Spotify’s content challenge was foreshadowed by a dust-up in 2018 over the streaming service’s decision to remove R&B star R. Kelly and rapper XXXTentacion from playlists and algorithmic recommendations to listeners based on abuse allegations against the artists.

The company introduced a “Hate Content and Hateful Conduct” policy that touched off a debate about whether streaming services should punish artists for alleged bad behavior. It drew criticism from across the music industry; some said the policy appeared to target only Black men who hadn’t at the time been convicted of crimes. Spotify withdrew the policy three weeks later. The company said in a blog post at the time that its job isn’t to regulate artists.

As part of its ambition to become an audio giant, Spotify has invested in dozens of people working on its trust-and-safety team, plus outside support and advisers, said the people inside the company. But that happened largely in private. “It was the one thing not debated and not openly discussed,” said the executive.

Spotify, the largest streaming company by subscriptions, has been pushing aggressively into podcasting in the past few years in a bid to differentiate itself from other services and become more profitable. It spent $100 million in 2020 to exclusively host Mr. Rogan’s podcast, according to people familiar with the matter, among other high-profile deals.

Spotify’s trust-and-safety team develops and enforces its content policies, the company said. It also seeks advice from outside experts who specialize in hate speech, extremism and misinformation, and is investing in how to moderate its content using algorithms and people.

When it became clear by the weekend that Spotify needed to offer a broader public response, its global head of music, Jeremy Erlich, stepped up calls to artists and labels about the protest.

Dawn Ostroff,

the chief content and advertising business officer who has spearheaded Spotify’s podcast expansion, connected with podcasters.

“We haven’t been transparent around the policies that guide our content more broadly,” said Mr. Ek in a blog post Sunday. “It’s become clear to me that we have an obligation to do more to provide balance and access to widely accepted information from the medical and scientific communities guiding us through this unprecedented time.”

The company made public its policies, which it didn’t alter, and created a Covid-19 information hub. It said it would begin tagging Covid-19 related content with an advisory pointing users to that health-and-science hub. Teams inside Spotify worked through the night all weekend on the advisories, which began to roll out early this week, according to people inside the company.

Spotify didn’t remove any of Mr. Rogan’s vaccine-related episodes. While Spotify previously removed more than 40 of his episodes for policy violations, none of them has been related to the pandemic, said a person inside the company.

Mr. Ek in his blog indicated his commitment to open dialogue and an all-creators-welcome ethos. He personally disagrees with many on his service, he said, adding that “it is important to me that we don’t take on the position of being content censor.”

At other platforms, such as Facebook or YouTube, executives have also struggled to balance being open to all voices with being safe for users. Over the years, they have implemented extensive content policies and created teams to flag material they deem inappropriate or dangerous. Many tech platforms have been called on to answer to regulators and lawmakers about ways to prevent the dissemination of information that is widely considered false. In some cases, the platforms ban or suspend users.

Sunday night, Mr. Rogan posted a conciliatory video to his Instagram, pledging to be more balanced and informed about controversial topics and guests. The post was Mr. Rogan’s own initiative, but came as a relief to people inside Spotify. “It’s a strange responsibility to have this many viewers and listeners,” he said in the video. “I’m going to do my best to balance things out.”

Record executives said they felt Mr. Rogan’s response was genuine and pointed out that he addressed Mr. Young directly—a human element they found missing from Spotify’s response.

Since the beginning of Mr. Rogan’s deal with Spotify, he has emphasized on social media and his podcast that he and his team maintain control over the show. Spotify doesn’t produce or edit the show, it doesn’t approve guests or topics, and it doesn’t review the content before it goes live, the company has said.

At a town-hall-style meeting Wednesday, Spotify executives reiterated to employees that the company acts as a platform that distributes Mr. Rogan’s show rather than a producer or publisher, according to a transcript of the meeting. Mr. Ek said in the meeting that some employees feel hurt by the content and said it was important for them to understand why the company struck a deal with Mr. Rogan—and how effective it has been for Spotify’s growth.

“The Joe Rogan Experience” is the No. 1 show in 93 markets, Mr. Ek said during the interview Wednesday. In 2021, Mr. Rogan’s show was the most-listened-to podcast every month in more than 30 markets, including in the U.S., said a person familiar with the matter. Mr. Rogan’s listeners have grown by 75% from the time he joined Spotify’s platform in September 2020 to December 2021, this person said.

Importantly for Spotify’s business, Mr. Rogan’s listeners are highly engaged—they return to Spotify to listen more, and tend to listen to other content beyond his show, the company has said. In short, Mr. Rogan’s show has been crucial to making Spotify the top U.S. podcast platform by listeners, according to audio data provider Edison Research.

“Obviously with 11 million creators there’s a lot of discourse, there’s a lot of things here I don’t agree with, a lot of people might even find offensive too,” Mr. Ek said in the interview. “And yeah, that’s part of being a platform.”

Write to Anne Steele at Anne.Steele@wsj.com and John Jurgensen at john.jurgensen@wsj.com