GLASGOW—Organizers of the COP26 United Nations climate summit welcomed one of their highest-profile critics Friday: Greta Thunberg.

Ms. Thunberg is headlining an hourslong protest march and rally in Glasgow that kicked off early Friday. Thousands of mostly young protesters, carrying colorful banners and sometimes accompanied by their parents, marched from Glasgow’s Kelvingrove Park to the city center.

Organizers...

GLASGOW—Organizers of the COP26 United Nations climate summit welcomed one of their highest-profile critics Friday: Greta Thunberg.

Ms. Thunberg is headlining an hourslong protest march and rally in Glasgow that kicked off early Friday. Thousands of mostly young protesters, carrying colorful banners and sometimes accompanied by their parents, marched from Glasgow’s Kelvingrove Park to the city center.

Organizers of the two-week summit have called Friday “Youth and Public Empowerment” day, clearing out much of the technical briefings and news conferences that have filled most of the summit so far. That has provided another global platform for Ms. Thunberg and a handful of other high-profile climate activists, who supporters say have used their youth and social-media savvy to help broaden support for climate change action.

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Ms. Thunberg shot to fame three years ago as a schoolgirl who cut classes to protest what she said was inaction on climate change. She moved on to bluntly dress down world leaders. More recently, she has taken aim at the U.N. climate summit process itself, accusing it of being a talking shop with few concrete accomplishments to show for itself.

On the eve of Friday’s rally, Ms. Thunberg called the summit “a two week celebration of business as usual and blah blah blah” on Twitter.

“Blah, blah, blah is completely true, that is what world leaders do,” said Amanda Randall, a 59-year-old artist who had traveled from England to the protest march.

Many diplomats say they are making steady progress on many fronts in trying to reach deals that will lower global emissions to levels scientists hope will curb global warming. Critics say progress so far is incremental.

The U.K., the summit’s host country, said it welcomes the dialogue with demonstrators.

“The U.K. is committed to hosting an inclusive COP. Ensuring that the voices of those most affected by climate change are heard is a priority,” a spokeswoman for the event said.

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While not part of any formal negotiations at the summit, Ms. Thunberg has sometimes stolen the show from world leaders, diplomats and technocrats. On Monday, the first day of the summit, she was mobbed by supporters as she emerged from Glasgow’s main train station. On Wednesday, she slipped into a briefing about carbon offsets, triggering a rush of delegates trying to get a glimpse of her, Bloomberg reported.

Now 18, Ms. Thunberg has appeared to change her tone in subtle ways during the summit, one of the first big events in which she hasn’t been accompanied by her father, Svante Thunberg. Ahead of Friday’s rally, she triggered an online debate about her increasingly salty language. She was asked on Twitter if she would commit to “net-zero” bad language, echoing climate-talk jargon for how countries account for their carbon emissions.

She answered with the sort of time frame most big countries have given for when they will get net carbon emissions to zero. The U.S. for example has promised to get to net zero emissions by 2050 and reduce them by 50%-52% by 2030. Ms. Thunberg promised on Twitter to stop swearing “by 2052 with a 39, 78% reduction by 2034.”

The evolution in her public persona continues to resonate with young activists who have energized the push for action on climate in recent years, according to Richard Black, a research fellow at the Grantham Institute, which researches climate change. Now “she is becoming more direct in the way she speaks,” he said.

“My parents, who are in their 70s, think she should be keeping her nose out of that sort of thing as an 18-year-old,” said Scott Muirhead, 38, who works in a call center in Glasgow, as he headed to his first climate protest. “I have grown up with climate change. When I was at school we got school projects on climate change so we’re more aware of it.”

Daisy Earl, 19, came up by train from Leeds to join the rally. She says she’s fed up by what she calls greenwashing. “It’s all talk, no action, they keep making pledges but don’t do anything,” she said.

While Ms. Thunberg’s status and influence have grown, she continues to operate largely independent of any official support infrastructure, according to people who have worked with her. Ms. Thunberg relies on a loose web of fellow activists, nongovernment agencies and scientists to help pro-bono to inform and organize her campaign.

She is staying in an apartment in Glasgow provided by an activist friend. Her train tickets from Stockholm were paid for by her parents. The setup can be chaotic at times, people who work with her say. Her father says he sometimes has to urge her to meet with high-profile dignitaries.

The Fridays For Future movement she founded isn’t a legal entity and instead relies on local volunteers to run their own campaigns in different countries. Ms. Thunberg sometimes gets logistical help from environmental groups such as Greenpeace. Members of the Global Strategic Communications Council, a nonprofit network of communications professionals, help with media work.

The law firm Hausfeld & Co LLP says it helped with some projects pro-bono, including when she joined a complaint to a U.N. committee stating that several nations were violating the human rights of children by not doing more to combat climate change. The U.N. committee said it couldn’t rule on the complaint.

In 2019, her parents set up a foundation to handle prize money and royalties earned by their daughter. Ms. Thunberg has so far won awards worth over $1 million for her campaigning.

The Greta Thunberg Foundation says it awards grants to promote “ecological, climatological and social sustainability.” Last year it distributed around €620,000, equivalent to around $715,000, to 16 organizations, including Unicef and Greenpeace. It is chaired by Paulina von Euler, the chief executive officer of von Euler & Partners AG, a Swedish investment company.

—Matthew Dalton in Glasgow contributed to this article.

Write to Max Colchester at max.colchester@wsj.com and Sha Hua at sha.hua@wsj.com